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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=−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

1 answer

To find the values of \( a \) and \( b \) using the provided arithmetic sequence formula \( a_n = -8 + (n-1) \cdot 2 \), we first need to determine the appropriate values of \( n \) for \( x = 2 \) and \( x = 4 \).

  1. For \( x = 2 \): We can set \( n = 2 \) since it's the second term. \[ a_2 = -8 + (2-1) \cdot 2 = -8 + 1 \cdot 2 = -8 + 2 = -6 \] So, \( a = -6 \).

  2. For \( x = 4 \): We set \( n = 4 \) since it's the fourth term. \[ a_4 = -8 + (4-1) \cdot 2 = -8 + 3 \cdot 2 = -8 + 6 = -2 \] So, \( b = -2 \).

From the calculations above, we find that:

  • \( a = -6 \)
  • \( b = -2 \)

The correct response is: a equals negative 6; b equals negative 2.