CPM Homework Help : CCA Problem 5-122

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

Hint 1:

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

Step 1:

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

Step 2:

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

Step 3:

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

Answer:

$t(n) = −188n + 2560$

Hint 2:

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