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Arithmetic Sequences Quick Check
4 of 54 of 5 Items
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=−10
; b=−8
a equals negative 10 ; b equals negative 8

a=−6
; b=−2
a equals negative 6 ; b equals negative 2

a=−12
; b=−10
a equals negative 12 ; b equals negative 10

a=−15
; b=−13
a equals negative 15 ; b equals negative 13
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1 answer

To find the missing values \( a \) and \( b \) in the table using the arithmetic sequence formula given, we need to determine the values of \( n \) that correspond to \( x = 2 \) and \( x = 4 \).

The formula for the arithmetic sequence is:

\[ a_n = -8 + (n-1) \cdot 2 \]

  1. For \( x = 2 \):

    • Set \( n = 1 \) (since it's the first term): \[ a_1 = -8 + (1-1) \cdot 2 = -8 + 0 = -8 \] So, \( a = -8 \).
  2. For \( x = 4 \):

    • Set \( n = 2 \) (since this is the second term): \[ a_2 = -8 + (2-1) \cdot 2 = -8 + 2 = -6 \] So, \( b = -6 \).

Thus, the values of \( a \) and \( b \) are:

  • \( a = -6 \)
  • \( b = -4 \)

Since none of the options exactly match the values, it's possible I may have misinterpreted the sequence definition or terms associated with it. However, based on the arithmetic sequence calculations:

  • From above:
    • It might appear you are working with the differences or adjustments to the values leading to \( a \) outputs from different assignments.

For confirmation, the closest values you could possibly use would have been based directly on alterations in the sequence or step derivations per conditions applied.

Hence neither options of \( a=-10, b=-8 \) nor corresponding options of \( a=-15, b=-13\) yield successsful paths within these derived terms.

Refinements to seek here yield from continuation on outlining or establishing proper sequences as inherent arithmetic examples.

Feel free to follow up if assistance is needed with the existing formulations!