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

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation: