Chapter SH, Problem 10.15EP

To determine

To find: The first five terms of each sequence.

Answer to Problem 10.15EP

The first five terms of the sequence are 6, 27, 111, 447 and 1791.

Explanation of Solution

Given:

It is given that $a_1=6$ and $a_{n+1}=4a_n+3$ .

Calculation:

The first term is $a_1=6$ .

Find the second term as follows.

  $\begin{array}{c}{a}_2=4a_1+3\\ =4\left(6\right)+3\\ =24+3\\ =27\end{array}$

Find the third term as follows.

  $\begin{array}{c}{a}_3=4a_2+3\\ =4\left(27\right)+3\\ =108+3\\ =111\end{array}$

Find the fourth term as follows.

  $\begin{array}{c}{a}_4=4a_3+3\\ =4\left(111\right)+3\\ =444+3\\ =447\end{array}$

Find the fifth term as follows.

  $\begin{array}{c}{a}_5=4a_4+3\\ =4\left(447\right)+3\\ =1788+3\\ =1791\end{array}$

Therefore, the first five terms of the sequence are 6, 27, 111, 447 and 1791.