How many terms of G.P. 3, 32, 33, &helli | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Answer:

The given G.P. is 3, 3², 3³, …

Let n terms of this G.P. be required to obtain the sum as 120.

$S subscript n space equals space fraction numerator a open parentheses r to the power of n space minus space 1 close parentheses over denominator r minus 1 end fraction$

Here, a = 3 and r = 3

∴ $S subscript n space equals space 120 space equals space fraction numerator 3 space open parentheses 3 to the power of n space minus 1 close parentheses over denominator 3 minus 1 end fraction rightwards double arrow 120 space equals space fraction numerator 3 open parentheses 3 to the power of n space minus 1 close parentheses over denominator 2 end fraction rightwards double arrow fraction numerator 120 space cross times 2 over denominator 3 end fraction space equals space 3 to the power of n space minus 1 rightwards double arrow 3 to the power of n space minus 1 space equals space 80 rightwards double arrow 3 to the power of n space equals space 81 rightwards double arrow 3 to the power of n space equals space 3 to the power of 4$

∴ n = 4

Thus, four terms of the given G.P. are required to obtain the sum as 120.

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Reference examples and data from the chapter when answering questions about Sequence and Series.
Review previous year question papers to get an idea of how such questions may be framed in exams.
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Comments

Salome
2023-06-28 20:17:39

Kindly tell us what r means

HARISH N BIDARI
2023-02-03 23:04:52

Thank you sir/medam...this answer is helpful to us...ðððð

HARISH N BIDARI
2023-02-03 23:02:46

Thank you sir/medam...this answer is helpful to us...ðððð

Riya prasad
2021-10-30 07:22:14

Very good ðð

Sameer sharma
2019-11-04 09:10:53

Thanks for solving the question

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 13: How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?....

How many terms of G.P. 3, 32, 33, &helli | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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