Chapter 3.6, Problem 3BGP

To determine

To find the 15th term of the sequence.

Answer to Problem 3BGP

  $-179$

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 $-10-3=-13.$

Applying the above formula,

  $\begin{array}{c}{t}_{15}=3+(15-1)(-13)\\ =3+14\times (-13)\\ =179\end{array}$

Conclusion:

Therefore, the 15^th term of the given sequence is $179$ .