### Home > A2C > Chapter 2 > Lesson 2.2.3 > Problem 2-153

2-153.

Find the formula for *t*(*n*) for the arithmetic sequence in which *t*(15) = 10 and *t*(63) = 106. Homework Help ✎

Visualize the sequences as two points on a graph, (15, 10) and (63, 106).

Finding the common difference is the same as finding the constant rate of change of a line, the slope.

Use the slope or common difference and one of the points, say (15, 10) to substitute into *t*(*n*) = *mn* + *b*. And solve: 10 = 2(15) + *b*

*t*(*n*) = 2*n* − 20