Explanation Formula used: The geometric sequence is, a , a r , a r 2 , a r 3 , … , a r n , where a is the first term of the sequence and r is the common ratio. The formula to find the last term of the sequence is a n = a r n − 1 . Calculation: The third root of every term of a geometric sequence is also geometric sequence because the condition is applied to all the numbers in the sequence. So, the common ratio of the resulting sequence must be same. It is proved by using the following counter example. Consider the geometric sequence, 27 , 216 , 1728 , 13824 , 110592 which has the common ratio of 8. Take the cube root on every term of the geometric sequence, 27 , 216 , 1728 , 13824 , 110592

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ISBN: 9780137657988

Author: BILLSTEIN

Publisher: INTER PEAR

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 8.CR, Problem 29CR

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Whether the statement “If we take the third root of every term of a geometric sequence is the resulting sequence also geometric” is true or false. If it is true find the ratio and justify the answer.

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Chapter 8.CR, Problem 28CR

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Whether the statement “If we take the third root of every term of a geometric sequence is the resulting sequence also geometric” is true or false. If it is true find the ratio and justify the answer.

Solution Summary: The author explains that if the statement "If we take the third root of every term of a geometric sequence is the resulting sequence also geometric" is true or false.

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To find: Whether the statement “If we take the third root of every term of a geometric sequence is the resulting sequence also geometric” is true or false. If it is true find the ratio and justify the answer.

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Chapter 8 Solutions

To find:

Whether the statement “If we take the third root of every term of a geometric sequence is the resulting sequence also geometric” is true or false. If it is true find the ratio and justify the answer.