### Home > CCA2 > Chapter Ch3 > Lesson 3.1.3 > Problem3-48

3-48.

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

Visualize the sequence 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 $t(n)=2n+b$. Then solve: $10=2(15)+b$

$t(n)=2n−20$