Сумма n членов арифметической прогрессии

Вспомним... Дана последовательности чисел, представляющая собой арифметическую прогрессию:

3; 7; 11; ...; ...; ....

Забрать недостающие члены

• 11; 7; 3.

• 13; 17; 21.

• 15; 19; 23.

• 10; 21; 31.

Вспомним... Из предложенных последовательностей выберите те, которые являются арифметическими прогрессиями.

• 4; 4; 4; 4; 4; 4; ...; ...;

• 4; 8; 16; 32; 64; 128; ...; ...;

• 4; 8; 12; 16; 20; 24; ...; ...;

• 1; 4; 9; 16; 25; 36; ...; ...;

Вспомним... Для арифметической прогрессии _n : -7; -2; 3; 8; 13; ... Появляется ₁₀₁

• 493

• 106

• 1234

• 777

Первый член арифметической прогрессии равенства 2, а пятый равенство 10. Какой из предложенных формул будет описываться последовательностью последовательности?

• ${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">а</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}$a_n=2+2\влево(n-1\вправо)=2n $${а}_{}знак\; равно2+2\left(н-1\right)знак\; равно2н$$

• ${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">а</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">10</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">8</span></span></span></span>}$a_n=10+2\влево(n-1\вправо)=2n+8 $${а}_{}знак\; равно10+2\left(н-1\right)знак\; равно2н+8$$

• ${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">а</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">10</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">10</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}$a_n=2+10\влево(n-1\вправо)=10n $${а}_{}знак\; равно2+10\left(н-1\right)знак\; равно10н$$

• ${\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">а</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">10</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">10</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">18</span></span></span></span>}$a_n=2+10\влево(n-2\вправо)=10n-18 $${а}_{}знак\; равно2+10\left(н-2\right)знак\; равно10н-18$$

Задана последовательность чисел 1; 2; 3; 4; 5; 6; 7; 8; 9; 10. Отображение количества всех серий по этой серии

• 100

• 55

• 33

• 70

Арифметическая прогрессия${\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">а</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}$а_n=4n+3 $${а}_{}знак\; равно4н+3$$ , найдите${\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">С</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">20</span></span></span></span>}}$С_{20} $${С}_2$$

• 2519

• 83

• 860

• 900

Арифметическая прогрессия${\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">а</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">5</span></span></span></span>}$а_n=2n+5 $${а}_{}знак\; равно2н+5$$ , наличествует множество серий серий с 15-го по 30-й.

• 30

• 750

• 800

• 960

сумма двадцати первых серий рифметической прогрессии${\mathrm{<span\; class="katex-container"\; data-idx="4"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">с</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="4"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}}$с_n $${с}_{}$$ , если известно, что${\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">с</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span><span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">8</span></span></span></span>}$с_4=-8 $${с}_{}знак\; равно-8$$ , а${\mathrm{<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">с</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">17</span></span></span></span>}}<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">13</span></span></span></span>}$с_{17}=13 $${с}_1знак\; равно13$$ .

• 105

• 89

• 50

• 69

Внешний вид первого члена арифметической прогрессии${\mathrm{<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">у</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="3"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">н</span></span></span></span>}}$д_н $${у}_{}$$ , если известно, что${\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">у</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">15</span></span></span></span>}}<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="1"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">47</span></span></span></span>}$у_{15}=47 $${у}_1знак\; равно47$$ ,${\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">С</span></span></span></span>}}_{\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">15</span></span></span></span>}}<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">знак\; равно</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="2"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">375</span></span></span></span>}$S_{15}=375 $${С}_1знак\; равно375$$

(a)  

Сумма всех натуральных чисел кратных 6, но не кратных 216

(a)