Arithmetic Sequences Check-In

Arithmetic Sequences Check-In

(1/27/2021)

Fill in the Blanks

What is the next term in the sequence:

0, 3, 8, 15, 24, _

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What is the next term in the sequence:

0, 5, 5, 10, 15, 25, _

Fill in the Blanks

What is the next term in the sequence:

10, 1100, 111000, 11110000, _

Fill in the Blanks

What is the next term in the sequence:

3, 6, 9, 12, _

Multiple Select

2.) Which (if any) of the previous patterns are Arithmetic Sequences?

• a

• b

• c

• d

What makes a sequence arithmetic?

If each term is found by adding or subtracting the same number each time!

Fill in the Blanks

3.) Using the recursive formula, find a₂:

a₁ = 5

a_n = 3(a_n-1) + 4

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4.) Using the recursive formula, find a₂:

a₁ = 20

a_n = a_n-1 + 15

How do we use recursive formulas?

• When writing the formula, we only change the "m" value - - - - - - - a_n = a_n-1 + m

• When using the formula, we only plug in values for "a_n-1" - - - - - - - a_n = a_n-1 + m

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5.) What is the value of a₁ in the sequence:

-9, -3, 3, 9, ...

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5.) What is the common difference (m) of the sequence:

-9, -3, 3, 9, ...

5.) For the sequence -9, -3, 3, 9...

• Explicit Formula: a_n = -9 + 6(n-1) or a_n = 6n -15

• Recursive formula: a_n = a_n-1 + 6

Fill in the Blanks

5.) Find a₃₈ using the explicit formula a_n = -9 + 6(n-1)

Fill in the Blanks

5.) Find the sum of the first 38 terms

6.) 108, 88, 68, 48, ...

• Recursive Formula: a_n = a_n-1 - 20

• Explicit Formula: a_n = 108 - 20(n - 1)

• a₃₁ = -492

• The sum of the first 31 terms:  $s_{31}=\frac{31}{2}\left(108-492\right)=-5952$  

7.) a₁₂= 32.25, a₁₃= 39.5, a₁₄= 43.75

• Recursive Formula: a_n = a_n-1 + 4.25

• Explicit Formula: a_n = a₁ + 4.25(n - 1)

• Pick a given value to find a1:

•  $\ \ \ \ a_{12}=32.25\ =\ a_1+4.25\left(12-1\right)$  

•  $\ \ \ \ \ \ \ \ \ \ \ \ \ \ 32.25\ =\ a_1+46.75$  

•  $\ \ \ \ \ \ \ \ \ \ \ \ \ \ 14.5\ =\ a_1$  

Find the missing values of the sequence:

• 8.) 2, a₂, a₃, 23, ...

• a₂ = 9

• a₃ = 16

• 9.) 84, a₂, a₃, a₄, 32, ...

• a₂ = 71

• a₃ = 58

• a₄ = 45

Skip a few... 13.) $\sum_{i=4}^{10}120-11i$  

• Our first number: 120 - 11(4) = 120 - 44 = 76

• Our last number: 120 - 11(10) = 120 - 110 = 10

• Our total number of terms: 4th, 5th, 6th, 7th, 8th, 9th, 10th = 7 total

•  $\frac{n}{2}\left(first+last\right)=\frac{7}{2}\left(76+10\right)=3.5\left(86\right)=301$  

Skip a few... 15.) a₁ = 25 and d = 11. Which term of the sequence is 212

•  $a_n=a_1+m\left(n-1\right)$  

•  $212\ =\ 25\ +\ 11\left(n-1\right)$  

•  $212\ =\ 25\ +11n-11$  

•  $212\ =\ 14\ +\ 11n$  

•  $198\ =\ 11n$  

•  $18\ =\ n$  

• 212 is the 18th term in the sequence.