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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
a equals negative 6 ; b equals negative 2

1 answer

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 \( n \) values corresponding to the \( x \) values given in the table.

  1. Determine \( n \) for \( x = 2 \):

    • Setting \( x = 2 \) and solving for \( n \): \[ n = \frac{x + 8}{2} \] So, for \( x = 2 \): \[ n = \frac{2 + 8}{2} = \frac{10}{2} = 5 \]

  2. Calculate \( a \) (when \( n = 5 \)): \[ a = a_5 = -8 + (5 - 1) \cdot 2 = -8 + 4 \cdot 2 = -8 + 8 = 0 \]

  3. Determine \( n \) for \( x = 4 \):

    • For \( x = 4 \): \[ n = \frac{4 + 8}{2} = \frac{12}{2} = 6 \]

  4. Calculate \( b \) (when \( n = 6 \)): \[ b = a_6 = -8 + (6 - 1) \cdot 2 = -8 + 5 \cdot 2 = -8 + 10 = 2 \]

Now, we will summarize the results:

  • \( a = 0 \)
  • \( b = 2 \)

None of the responses given in the options match \( a = 0 \) and \( b = 2 \). Thus, if we strictly follow through the calculations, neither of the provided options can be accepted as correct.

However, there seems to be some discrepancy possibly due to different interpretations or calculations. Please review the methodology or provide corrections if required.