The geometric sequence ; is defined by the formula: a i a 1 =10 a i =a i-1 * 9/10 Find the sum of the first 75 terms in the sequence .

Question:

The geometric sequence ; is defined by the formula: ; Find the sum of the first 75 terms in the sequence .

Step-by-step explanation:

Given

Required

Find the sum of 75 terms

Given that the sequence is geometric;

First, the common ratio has to be calculated;

The common ratio is defined as follows;

Let

So,

becomes

Divide through by

Recall that

So,

Given that r < 1;

The sum of n terms is calculated as thus;

To calculate the sum of the first 75 terms, we have the following parameters

becomes

$15 each

step-by-step explanation:

$45/3 children= $15 each