Chapter 7.10, Problem 4CYU

To determine

The recursive formula for the given sequence.

Answer to Problem 4CYU

The recursive formula is $a_1=4$ , $a_n=3a_{n-1}$ , $n\ge 2$ .

Explanation of Solution

Given information: The sequence given 4, 12, 36, 108, ….

Calculation:

The first term given = 4.

  $\therefore a_1=4$

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

So we can write,

  $\begin{array}{l}{a}_2=12=4\times 3=a_1\times 3=3a_1\\ a_3=36=12\times 3=a_2\times 3=3a_2\\ a_4=108=36\times 3=a_3\times 3=3a_3\end{array}$

  $\therefore$ We can write, $a_n=3a_{n-1}$

The recursive formula for the given sequence is $a_1=4$ , $a_n=3a_{n-1}$ , $n\ge 2$ .