Arithmetic Sequences Quick Check

Question

4 of 54 of 5 Items
Question
Use the table to answer the question.

x y
2 a
4 b
Use the arithmetic sequence formula an=−8+(n−1)⋅2 to find the missing values in the table.

(1 point)
Responses

a=−10; b=−8
a equals negative 10 ; b equals negative 8

a=−12; b=−10
a equals negative 12 ; b equals negative 10

a=−6; b=−2
a equals negative 6 ; b equals negative 2

a=−15; b=−13
a equals negative 15 ; b equals negative 13
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Answer 1

To find the missing values \(a\) and \(b\) in the table using the arithmetic sequence formula \(a_n = -8 + (n-1) \cdot 2\), we need to calculate the values of the sequence at \(n = 2\) and \(n = 4\).

1. For \(n = 2\): \[ a_2 = -8 + (2-1) \cdot 2 \] \[ a_2 = -8 + 1 \cdot 2 \] \[ a_2 = -8 + 2 = -6 \] Thus, \(a = -6\).

2. For \(n = 4\): \[ a_4 = -8 + (4-1) \cdot 2 \] \[ a_4 = -8 + 3 \cdot 2 \] \[ a_4 = -8 + 6 = -2 \] Thus, \(b = -2\).

So, the missing values are:

• \(a = -6\)
• \(b = -2\)

The correct response is: a = -6; b = -2.