Chapter 7.10, Problem 1CYU

To determine

To Find: The first five terms of each sequence $a_1=16,a_n=a_{n-1}-3,n\ge 2$

Answer to Problem 1CYU

First five terms of the sequence are $a_1=16,a_2=13,a_3=10,a_4=7\&a_5=4$

Explanation of Solution

Given information:

  $a_1=16,a_n=a_{n-1}-3,n\ge 2$

Concept and Formula Used:

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

Calculation:

It is given that

  $\begin{array}{l}{a}_n=a_{n-1}-3,n\ge 2\\ \text{Put }n=2\\ a_2=a_{2-1}-3\\ a_2=a_1-3\\ \text{As }{a}_1=16\\ a_2=16-3=13\\ \text{Now put }n=3\text{ in }{a}_n=a_{n-1}-3,n\ge 2\\ a_3=a_{3-1}-3\\ a_3=a_2-3\\ \text{As }{a}_2=13\\ a_3=13-3=10\\ \text{Now put }n=4\text{ in }{a}_n=a_{n-1}-3,n\ge 2\\ a_4=a_{4-1}-3\\ a_4=a_3-3\\ \text{As }{a}_3=10\\ a_4=10-3=7\\ \text{Now put }n=5\text{ in }{a}_n=a_{n-1}-3,n\ge 2\\ a_5=a_{5-1}-3\\ a_5=a_4-3\\ \text{As }{a}_4=7\\ a_5=7-3=4\end{array}$

Conclusion:

First five terms of the sequence are $a_1=16,a_2=13,a_3=10,a_4=7\&a_5=4$