Question

Given the explicit formula for an arithmetic sequence find the first five terms and the

52nd term:
an = -5n-22

Answer 1

a₁ = -27

a₂ = -32

a₃ = -37

a₄ = -42

a₅ = -47

a₅₂ = -282

Explanation:

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

Given explicit formula:

`a_n=-5n-22`

To find the first 5 terms, substitute n = 1 through 5 into the given formula:

`\begin{aligned}\implies a_1&=-5(1)-22\\&=-5-22\\&=-27\end{aligned}`

`\begin{aligned}\implies a_2&=-5(2)-22\\&=-10-22\\&=-32\end{aligned}`

`\begin{aligned}\implies a_3&=-5(3)-22\\&=-15-22\\&=-37\end{aligned}`

`\begin{aligned}\implies a_4&=-5(4)-22\\&=-20-22\\&=-42\end{aligned}`

`\begin{aligned}\implies a_5&=-5(5)-22\\&=-25-22\\&=-47\end{aligned}`

To find the 52nd term, substitute n = 52 into the given formula:

`\begin{aligned}\implies a_(52)&=-5(52)-22\\&=-260-22\\&=-282\end{aligned}`