Chapter 7.8, Problem 7LC

To determine

To Write: Write the explicit and recursive formula for the given geometric sequence.

Answer to Problem 7LC

The recursive formula is $a_n=a_{n-1}.\left(\frac{2}{3}\right);a_1=162$

The explicit formula is $a_n=162.{\left(\frac{2}{3}\right)}^{n-1}$

Explanation of Solution

Given information : The given sequence is 3, 6, 12, 24, …..

Here the geometric sequence is 3, 6, 12, 24, …..

Here the first term is $a_1=3$ and common ratio = $r=\frac{6}{3}=2$

The recursive formula is

  $a_n=a_{n-1}.r;a_1=3$

Now, substituting the value of r

  $a_n=a_{n-1}.\left(2\right);a_1=3$

The explicit formula is

  $a_n=a_1{r}^{n-1}$

Substituting the value of a and r

  $a_n=3.{\left(2\right)}^{n-1}$