Chapter 7, Problem 78SGR

To determine

The first five terms of a sequence.

Answer to Problem 78SGR

The first five terms are 3, 12, 30, 66, 138.

Explanation of Solution

Given information: Given first term $a_1=3$ , and also $a_n=2a_{n-1}+6$ , $n\ge 2$ .

Calculation:

First term $a_1=3$ and given $a_n=2a_{n-1}+6$ , $n\ge 2$ .

When n=2, second term

  $\begin{array}{l}{a}_2=2a_1+6\\ =2(3)+6\\ =6+6=12\end{array}$

When n=3, third term

  $\begin{array}{l}{a}_3=2a_2+6\\ =2(12)+6\\ =24+6=30\end{array}$

When n=4, fourth term

  $\begin{array}{l}{a}_4=2a_3+6\\ =2(30)+6\\ =60+6=66\end{array}$

When n=5, fifth term

  $\begin{array}{l}{a}_5=2a_4+6\\ =2(66)+6\\ =132+6=138\end{array}$

So, the first five terms are 3, 12, 30, 66, 138.