Chapter ISG, Problem 7.4STP

To determine

To calculate the third and fourth term

Answer to Problem 7.4STP

The third and fourth term are 360 and 216, respectively.

Explanation of Solution

Given information:

A geometric sequence is given.

First term is, $a1=1000$

N^th term formula is, $a_n=\frac{3a_{n-1}}{5}$

Formula used:

Substituting and solving

Calculation:

For the second term, substituting the values,

  $a_2=\frac{3a_{2-1}}{5}$

Substituting the value of first term,

  $a_2=\frac{3\times 1000}{5}$

On solving,

  $a_2=600$

For the third term, substituting the values,

  $a_3=\frac{3a_{3-1}}{5}$

Substituting the value of second term,

  $a_3=\frac{3\times 600}{5}$

On solving,

  $a_3=360$

For the fourth term, substituting the value,

  $a_4=\frac{3a_{4-1}}{5}$

Substituting the value of third term,

  $a_4=\frac{3\times 360}{5}$

On solving,

  $a_4=216$

Hence, the third and fourth term are 360 and 216, respectively.