Chapter 7, Problem 81SGR

To determine

The recursive formula for the given sequence.

Answer to Problem 81SGR

The recursive formula is $a_n=a_{n-1}+3(2^{n-2})$ .

Explanation of Solution

Given information:The sequence given 2, 5, 11, 23, ….

Calculation:

The first term given = 2.

  $\therefore a_1=2$

Second term $a_2=5$ , third term $a_3=11$ , fourth term $a_4=23$ .

So we can write,

  $\begin{array}{l}{a}_2=5=2+3=a_1+3=a_1+3(2^0)\\ a_3=11=5+6=a_2+6=a_2+3(2^1)\\ a_4=23=11+12=a_3+12=a_3+3(2^2)\end{array}$

$\therefore$ We can write, $a_n=a_{n-1}+3(2^{n-2})$