Question

Arithmetic Sequences Quick Check
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=−12; b=−10
a equals negative 12 ; b equals negative 10

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

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 values of \( a \) and \( b \) using the arithmetic sequence formula \( a_n = -8 + (n - 1) \cdot 2 \), we will calculate \( a \) when \( x = 2 \) (which corresponds to \( n = 2 \)) and \( b \) when \( x = 4 \) (which corresponds to \( n = 4 \)).

1. **Calculate \( a \) (when \( n = 2 \))**:
\[
a_2 = -8 + (2 - 1) \cdot 2 = -8 + 1 \cdot 2 = -8 + 2 = -6
\]

2. **Calculate \( b \) (when \( n = 4 \))**:
\[
a_4 = -8 + (4 - 1) \cdot 2 = -8 + 3 \cdot 2 = -8 + 6 = -2
\]

Thus, we have:
- \( a = -6 \)
- \( b = -2 \)

The corresponding response is:
- **a equals negative 6; b equals negative 2**.