Chapter 7.10, Problem 34HP

To determine

The recursive formula for the given sequence.

Answer to Problem 34HP

The recursive formula is $a_1=4$ , $a_n=2a_{n-1}+1$ .

Explanation of Solution

Given information: The sequence given 4, 9, 19, 39, 79, ….

Calculation:

The first term given = 4.

  $a_1=4$

Second term $a_2=9$ , third term $a_3=19$ , fourth term $a_4=39$ , fifth term $a_5=79$ .

So we can write,

  $\begin{array}{l}{a}_2=9=2\times 4+1=2a_1+1\\ a_3=19=2\times 9+1=2a_2+1\\ a_4=39=2\times 19+1=2a_3+1\\ a_5=79=2\times 39+1=2a_4+1\end{array}$

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

So the recursive formula is $a_1=4$ , $a_n=2a_{n-1}+1$