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

a=−6
; b=−2

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 proceed as follows:

1. **Find \( a \) when \( x = 2 \)**:
\[
a_2 = -8 + (2 - 1) \cdot 2 = -8 + 1 \cdot 2 = -8 + 2 = -6
\]
So, \( a = -6 \).

2. **Find \( b \) when \( x = 4 \)**:
\[
a_4 = -8 + (4 - 1) \cdot 2 = -8 + 3 \cdot 2 = -8 + 6 = -2
\]
So, \( b = -2 \).

Putting these together, we have:
- \( a = -6 \)
- \( b = -2 \)

The correct answer from the options provided is:
**a = −6; b = −2**.