Chapter 12.7, Problem 59STP

To determine

To find :missing value for arithmetic sequence, $n$.

Answer to Problem 59STP

  $15$

Explanation of Solution

Given information :

We know that, the given data is $a_4=18,a_n=95,d=7$

Formula Used:

  $a_n=a+(n-1)d$

Calculation:

  $\begin{array}{l}95=a+(n-1)7\\ 95=a+7n-7\\ 102=a+7n\mathrm{....}(1)\\ a_4=a+(4-1)d\\ 18=a+3(7)\\ a=18-21=-3\mathrm{.....}(2)\end{array}$

Using $\text{(1)}$ and $\text{(2)}$

  $\begin{array}{l}102=-3+7n\\ 7n=105\\ \Rightarrow n=\frac{105}{7}=15\end{array}$