Chapter 3.6, Problem 28PPS

To determine

To determine the position of a term of an arithmetic sequence.

Answer to Problem 28PPS

9^th

Explanation of Solution

Given:

The first four terms of an arithmetic sequence are $28,20,12\&4$ .

nth term = -36

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 sequence is

  $20-28=-8$

Let the nth term of the arithmetic sequence is $-36$ .

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

  $\Rightarrow a_n=28+(n-1)(-8)$  $[\because a=28\&d=-8]$

  $\begin{array}{l}\Rightarrow -36=36-8n\\ \Rightarrow 8n=36+36\\ \Rightarrow 8n=72\\ \Rightarrow n=9\end{array}$

Conclusion:

The 9^th term of the arithmetic function is $-36$ .