Chapter 3.6, Problem 40PFA

To determine

To determine the formula for the nth term.

Answer to Problem 40PFA

  $5n+12$

Explanation of Solution

Given:

Sequence:

  $17,22,27,\mathrm{32...}$

Formula used:

nth term of any arithmetic progression is given by the formula:

  $t_n=a+(n-1)d$

  $t_n=$ nth term

  $a=$ The first term of the arithmetic progression

  $d=$ The common difference of the arithmetic progression

Calculation:

The common difference of the arithmetic progression is:

  $22-17=5$

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

  $\Rightarrow a_n=17+(n-1)(5)$  $[\because a=17\&d=5]$

  $\begin{array}{l}\Rightarrow a_n=17+5n-5\\ \Rightarrow a_n=5n+12\end{array}$

The required nth term formula of the sequence is $a_n=5n+12$ .

Conclusion:

Hence, the missing part is $5n+12$ .