Question

AcellusFind a formula for the nth term in thisarithmetic sequence:a1 = 7, 22 = 4, a3 = 1, 24 = -2, ...דיan = [ ? ]n +=Enter

Answer 1

Arithmetic sequece formula:

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

Find the common difference (d): Subtract each term from the next term:

`\begin{gathered} 4-7=-3 \\ 1-4=-3 \\ -2-1=-3 \end{gathered}`

Common difference: d=-3

`a_n=7+(n-1)(-3)`

Simplify:

`\begin{gathered} a_n=7-3n+3 \\ \\ a_n=-3n+10 \end{gathered}`

Then, the formula for the given sequence is:

`a_n=-3n+10`