### Home > CCA2 > Chapter A > Lesson A.3.3 > ProblemA-117

A-117.

An arithmetic sequence has $t(8)=1056$ and $t(13)=116$. Write an equation for the sequence. What is $t(5)$?

The general equation for an arithmetic sequence is $t(n) = mn + b$.

Use $t(8) = 1056$ to write an equation.
$t(8) = m(8) + b \text{ or } 1056 = 8m + b$

Use $t(13) = 116$ to write another equation.

Solve the system of equations you wrote for $m$ and $b$.

$t(n) = −188n + 2560$

To find $t(5)$, substitute $5$ for $n$ in the equation that you wrote.