Use the table to answer the question.

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.
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
a equals negative 6 ; b equals negative 2

Answer 1

The arithmetic sequence formula provided is given as \( a_n = -8 + (n-1) \cdot 2 \). This formula will allow us to find the y-values (a and b) for the corresponding x-values (2 and 4) in the table.

Let's calculate the values:

1. For \( x = 2 \):

   • Here, \( n = 2 \).
   • Plugging this into the formula: \[ a_2 = -8 + (2 - 1) \cdot 2 = -8 + 1 \cdot 2 = -8 + 2 = -6. \] Thus, \( a = -6 \).

2. For \( x = 4 \):

   • Here, \( n = 4 \).
   • Plugging this into the formula: \[ a_4 = -8 + (4 - 1) \cdot 2 = -8 + 3 \cdot 2 = -8 + 6 = -2. \] Thus, \( b = -2 \).

So the values are:

• \( a = -6 \)
• \( b = -2 \)

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