Chapter ISG, Problem 7.9STP

To determine

To calculate the function for the given sequence.

Answer to Problem 7.9STP

The function for the given sequence is $f(x)=5{(1.2)}^{x-1}$

Explanation of Solution

Given information:

The sequence is 5, 6, 7.2, 8.64…

Formula used:

The formula for geometric sequence is,

  $a_n=a{r}^{n-1}$

Common ratio is,

  $r=\frac{a1}{a2}$

Calculation:

Substituting the values in common ratio formula,

  $r=\frac{6}{5}$

On solving,

  $r=1.2$

For function, substituting the geometric sequence formula,

  $f(x)=5{(1.2)}^{x-1}$

Hence, the function for the given sequence is $f(x)=5{(1.2)}^{x-1}$