Question

Question Use the table to answer the question. This table shows x-values with corresponding variables for y-values. 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=−15 ; b=−13 a equals negative 15 ; b equals negative 13 a=−6 ; b=−2 a equals negative 6 ; b equals negative 2 a=−10 ; b=−8

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 determine the values of \( n \) corresponding to \( x = 2 \) and \( x = 4 \).

1. **Finding \( a \) when \( x = 2 \)**:
- We need to find \( n \) such that \( x = 2 \).
- Since the first term corresponds to \( n=1 \), let’s substitute \( n = 1 \):
\[
a_1 = -8 + (1 - 1) \cdot 2 = -8 + 0 = -8
\]
- Thus, \( a \) corresponds to \( n = 1 \), and since \( x=2 \) corresponds to \( n=1 \), we find:
\[
a = -8
\]

2. **Finding \( b \) when \( x = 4 \)**:
- Next, we find \( n \) such that \( x = 4 \). Observe that if \( x \) increases by 2, we assume that \( n \) increases by 1.
- Hence, we set \( n = 2 \):
\[
a_2 = -8 + (2 - 1) \cdot 2 = -8 + 2 = -6
\]
- So, \( b \) corresponds to \( n = 2 \), and since \( x=4 \), we find:
\[
b = -6
\]

Putting this all together:
- \( a = -8 \)
- \( b = -6 \)

Since none of the provided answer options directly match \( a = -8 \) and \( b = -6 \), based on the options you've presented, you may want to recheck if there was a mistake in the problem or options.

For the context of your question:
- If we reconsider if we missed anything, here's the summary to validate:
- With \( n = 1 \) for \( x=2, \; a = -8 \)
- With \( n = 2 \) for \( x=4, \; b = -6 \)

Would you like to adjust or proceed further?