Chapter SH, Problem 7.34EP

To determine

To find first five terms of the sequence.

Answer to Problem 7.34EP

First five terms are $5,18.5,65.75,231.125,809.9375$

Explanation of Solution

Given information:

  $a_1=5$

The sequence is

  $a_n=3.5a_{n-1}+1,n\ge 2$

Calculation:

  $a_n=3.5a_{n-1}+1,n\ge 2\mathrm{.........}(1)$

  $a_n$ is $n^{th}$ term

Put $n=2$in equation (1)

  $a_2=3.5a_1+1$

On solving,

  $a_2=3.5(5)+1$

On solving,

  $a_2=18.5$

Put $n=3$in equation (1)

  $a_3=3.5a_2+1$

On calculation $a_2=18.5$ put in above

  $a_3=3.5(18.5)+1$

On solving,

  $a_3=65.75$

Put $n=4$in equation (1)

  $a_4=3.5a_3+1$

On calculation $a_3=65.75$ put in above

  $a_4=3.5(65.75)+1$

On solving,

  $a_4=231.125$

Put $n=5$in equation (1)

  $a_5=3.5a_4+1$

On calculation $a_4=231.125$ put in above

  $a_4=3.5(231.125)+1$

On solving,

  $a_5=809.9375$

Hence, first five terms are $5,18.5,65.75,231.125,809.9375$