Chapter 3.6, Problem 38PFA

To determine

To determine the formula for the nth term.

Answer to Problem 38PFA

D

Explanation of Solution

Given:

Sequence:

  $5,-3,-11,-\mathrm{19...}$

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:

  $-3-5=-8$

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

  $\Rightarrow a_n=5+(n-1)(-8)$  $[\because a=5\&d=-8]$

  $\begin{array}{l}\Rightarrow a_n=5-8n+8\\ \Rightarrow a_n=13-8n\end{array}$

The required nth term formula of the sequence is $a_n=13-8n$ .

Conclusion:

Hence, the correct option is D.