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Algebra 1
Found in: Page 596
Algebra 1

Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

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Short Answer

Find the next three terms in each geometric sequence.


The next three terms in the geometric sequence are 1,  1,  1.

See the step by step solution

Step by Step Solution

Step 1. State the concept used.

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.

The ration of 2nd term and first term is called the common ratio.

Step 2. Find the common ratio. 

The sequence: 1,1,1,1,.....

Each term in a geometric sequence can be expressed in terms of the first term a1 and the common ratio r. Since each succeeding term is formulated from one or more previous terms, this is a recursive formula.

First term a1=1 and the common ratio is:

r=  a2a1=1(1)=1

Step 3. Find the next three terms.

In order to calculate the next three terms of the geometric sequence substitute n=4,5,6 and -1 for a1 into the formula an=a1rn1.



In terms of a1 and r


Fourth term




Fifth term




Sixth term




Thus, next three terms of the sequence 1,1,1,1,..... are 1,  1,  1.

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