Chapter 7.10, Problem 3CYU

To determine

The recursive formula for the given sequence.

Answer to Problem 3CYU

The recursive formula is $a_1=1$ , $a_n=a_{n-1}+5$ , $n\ge 2$ .

Explanation of Solution

Given information: The sequence given 1, 6, 11, 16, ….

Calculation:

The first term given = 1.

  $\therefore a_1=1$

Second term $a_2=6$ , third term $a_3=11$ , fourth term $a_4=16$ .

So we can write,

  $\begin{array}{l}{a}_2=6=1+5=a_1+5\\ a_3=11=6+5=a_2+5\\ a_4=16=11+5=a_3+5\end{array}$

  $\therefore$ We can write, $a_n=a_{n-1}+5$

The recursive formula for the given sequence is $a_1=1$ , $a_n=a_{n-1}+5$ , $n\ge 2$ .