Chapter 3.6, Problem 3DGP

To determine

To determine the position of the term of the sequence.

Answer to Problem 3DGP

  $10\text{th}$

Explanation of Solution

Given:

Sequence:

  $3,-10,-23,-\mathrm{36...}$

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 first term of the sequence $(a)$ is $3$ .

The common difference of the sequence $(d)$ is: $(-10-3)=-13.$

Let,

The nth term of the sequence is $-114.$

Then,

  $\Rightarrow -114=3+(n-1)(-13)$  $[\because t_n=a+(n-1)d]$

  $\begin{array}{l}\Rightarrow -114-3=(n-1)(-13)\\ \Rightarrow -117=(n-1)(-13)\end{array}$

  $\Rightarrow 9=n-1$ [Dividing both the sides by $-13$ ]

  $\Rightarrow n=10$

Conclusion:

Therefore, the $10\text{th}$ term of the given sequence is $-114$ .