### Home > AC > Chapter 14 > Lesson 14.2.1.7 > Problem 2-104

2-104.

An arithmetic sequence has *t*(8) = 1056 and *t*(13) = 116. What is *t*(5) ? Homework Help ✎

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

Use *t*(8) = 1056 to write an equation.*t*(8) = *m*(8) + *b* or 1056 = 8*m* + *b*

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

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

*t*(*n*) = −188*n* + 2560

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