### Home > AC > Chapter 13 > Lesson 13.RE3-S > Problem2-153

2-153.

Find the formula for $t\left(n\right)$ for the arithmetic sequence in which $t\left(15\right) = 10$ and $t\left(63\right) = 106$.

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

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 $\left(15, 10\right)$ to substitute into $t\left(n\right) = mn + b$. And solve: $10 = 2\left(15\right) + b$

$t\left(n\right) = 2n − 20$