Chapter 3.6, Problem 38PFA

To determine

To Find: The value of $n^{th}$ term of an arithmetic progression.

Answer to Problem 38PFA

  $n^{th}$ term of an arithmetic progression is $a_n=-8n+13$ option ‘D’ is correct.

Explanation of Solution

Given information:

First four terms of an arithmetic sequence is $5,-3,-11\&-19$

Concept and Formula Used:

Arithmetic Sequence: The sequence with difference between successive terms is constant.

  $n^{th}$ term of an arithmetic progression is $a_n=a+\left(n-1\right)d$

Where ‘a’ is the first term and ‘d’ is the common difference.

Calculation:

It is given that four terms of an arithmetic sequence are $5,-3,-11\&-19$

As in arithmetic sequence the difference between successive terms is constant.

Therefore $d=-3-5=-8\&a=5$

The $n^{th}$ term of an arithmetic progression is

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ a_n=5+\left(n-1\right)\left(-8\right)\\ a_n=5-8n+8\\ a_n=13-8n\\ \text{or }{a}_n=-8n+13\end{array}$

Conclusion:

  $n^{th}$ term of an arithmetic progression is $a_n=-8n+13$ option ‘D’ is correct.