Question

Write an explicit formula for the sequence.

a^n+1=an+7, a^1=−22
A. a^n=7−22n
B. a^n=−22+7(n−1)
C. a^n=7−22(n−1)
D. a^n=−22+7n

Answer 1

`\textsf{B)} \quad a_n=-22+7(n-1)`

Explanation:

An explicit formula for a sequence allows you to find the nth term of the sequence.

A recursive formula for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

Given recursive rule:

`\begin{cases}a_(n+1)=a_n+7\\a_1=-22\end{cases}`

From the given recursive rule, we can see that each term is 7 more than the previous term. Therefore, the common difference between terms is d = 7.

Explicit formula

`a_n = a_1 + (n - 1)d`

Input the values of a₁ and d into the explicit formula:

`\implies a_n=-22+(n-1) \cdot 7`

`\implies a_n=-22+7(n-1)`

Therefore, the explicit formula for the given sequence is:

`\boxed{a_n=-22+7(n-1)}`