Arithmetic and Geometric Sequence

The most popular Geometric sequence studied by scientist, artists, and mathematicians, and musicians!

• Observing nature he came up with this sequence.​

• 1,1,2,3,4,5,8,13,21,34,55,89,144,

  233.... Each number before is added to the next number​

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​Applied Math

​Fibonacci Sequence

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​Sequences

​Sequence

a list of numbers that are related to each other by a rule.

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Some text here about the topic of discussion

​Term

The numbers in the sequence​

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Multiple Choice

What is the Rule for this sequence?
3, 7, 11, 15, ...

• +6
• +5
• +4
• +2

Multiple Choice

What is the Rule for this sequence?
97, 86, 75, 64, ...

• +8
• +11
• -11
• -8

Multiple Choice

Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

• 63, 72, 81
• 79, 88, 97
• 70, 79, 88
• 61, 70, 79

​Mathematical modeling and sequences

What would be the spending in the following years?

2011

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2015

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2018

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2022​

​Arithmetic Sequence​

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​Common difference​

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​Represented in the sequence formula

as d​

Multiple Choice

Find the common difference: -34, -29, -24, -19, ...

• d = -5
• d = 5
• d = -6
• d = 6

Multiple Choice

Sometimes sequences are described in subscript notation.

Given $$a_1=-5$$  and $$a_n=a_{n-1}+3$$  , what are the first 4 terms in the sequence?

• -5, -2, 1, 4

• -5, -8, -11, -14

• 3, -2, -7, -12

• 3, -15, 75, -375

Multiple Choice

Identify a₁ and d for the sequence
-5, -2, 1, 4, ...

• a₁ = 3 and d = -5
• a₁ = -8 and d = 3
• a₁ = -5 and d = 3
• a₁ = -5 and d = -3

Multiple Choice

Write the EXPLICIT rule for the arithmetic sequence

-10, -3, 4, 11,...

• a_n = 10n + 17

• a_n = 7n - 17

• a_n = -7n + 17

• a_n = 7n + 3

​Geometric Sequence​

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​Common ratio​

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​The amount by which we multiply each time.

Multiple Choice

What does r represent?

• Radical

• Common difference

• Common ratio

Multiple Choice

What does a₁ represent?

• Any term

• First term

• Last term

Multiple Choice

Find the common ratio for the geometric sequence.

• 1
• -1
• 7
• -7

Multiple Choice

Write the explicit formula for the geometric sequence.

• a_n = 4(3)^n-1
• a_n = 3(4)^n-1
• a_n = -4(3)^n-1
• a_n = 3(-4)^n-1

Poll

I can solve problems involving arithmetic and geometric sequence?

• YES! I GOT IT

• I KIND OF GOT IT,

• I NEED MORE HELP WITH IT

• I DO NOT UNDERSTAND IT AT ALL!