Chapter 14.7, Problem 1MRE

To determine

To find:Whether the sequence is arithmetic or geometric and then find the specified term of the sequence.

Answer to Problem 1MRE

The given series is an arithmetic progression and it ${21}^{\text{st}}$ term is $107$ .

Explanation of Solution

Given: $7,12,17,\mathrm{.......},t_{21}$ .

Check from common difference.

  $\begin{array}{c}12-7=17-12\\ 5=5\end{array}$

The common difference is same. So, the sequence is an arithmetic progression.

The expression for the $n^{\text{th}}$ term of an arithmetic sequence is given by.

  $a_n=a_1+\left(n-1\right)d$

Substitute the values in the above expression.

  $\begin{array}{c}{a}_{21}=7+\left(21-1\right)5\\ =7+100\\ =107\end{array}$

Therefore, the given series is an arithmetic progression and it ${21}^{\text{st}}$ term is $107$ .