Chapter 12.9, Problem 30E

To determine

To find: the value of $d$ for the arithmetic sequence.

Answer to Problem 30E

  $\frac{5}{2}$

Explanation of Solution

Given information:

  $\begin{array}{l}{a}_1=-6\\ a_{29}=64\end{array}$

Calculation:

The value of $d$ can be evaluated as shown below.

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ a_{29}=a_1+\left(29-1\right)d\left[\text{Put }n=29\right]\\ 64=-6+28d\\ 64+6=28d\\ 70=28d\\ d=\frac{70}{28}\\ =\frac{5}{2}\end{array}$

Thus, the value of $d$ is $\frac{5}{2}$ .