Question

Which of the following is an arithmetic sequence that could be modeled by an explicit formula expressed as a linear function? A. −1, −8, −27, −64, −125, … B. −5, −2, 3, 10, 19, … C. −5, −1, 3, 7, 11, … D. 1/2, 1/4, 1/8, 1/16, 1/32, …

Answer 1

C

Explanation:

Given

- 5, - 1, 3, 7, 11

There is a common difference d between consecutive terms, that is

11 - 7 = 7 - 3 = 3 - (- 1) = - 1 - (- 5) = 4

This indicates the sequence is arithmetic with explicit formula

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 5 and d = 4 , thus

`a_(n)` = - 5 + 4(n - 1) = - 5 + 4n - 4 = 4n - 9