Chapter 7.10, Problem 10PPS

To determine

To Find: The first five terms of each sequence $a_1=23,a_n=a_{n-1}+7,n\ge 2$

Answer to Problem 10PPS

First five terms of the sequence are $a_1=23,a_2=30,a_3=37,a_4=44\&a_5=51$

Explanation of Solution

Given information:

  $a_1=23,a_n=a_{n-1}+7,n\ge 2$

Concept and Formula Used:

To find the terms put the value of ‘n’.

Calculation:

It is given that

  $\begin{array}{l}{a}_1=23,a_n=a_{n-1}+7,n\ge 2\\ \text{Put }n=2\\ a_2=a_{2-1}+7\\ a_2=a_1+7\\ \text{As }{a}_1=23\\ a_2=23+7=30\\ \text{Now put }n=3\text{ in }{a}_n=a_{n-1}+7,n\ge 2\\ a_3=a_{3-1}+7\\ a_3=a_2+7\\ \text{As }{a}_2=30\\ a_3=30+7=37\\ \text{Now put }n=4\text{ in }{a}_n=a_{n-1}+7,n\ge 2\\ a_4=a_{4-1}+7\\ a_4=a_3+7\\ \text{As }{a}_3=37\\ a_4=37+7=44\\ \text{Now put }n=5\text{ in }{a}_n=a_{n-1}+7,n\ge 2\\ a_5=a_{5-1}+7\\ a_5=a_4+7\\ \text{As }{a}_4=44\\ a_5=44+7=51\end{array}$

Conclusion:

First five terms of the sequence are $a_1=23,a_2=30,a_3=37,a_4=44\&a_5=51$