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The sum of some terms of G.P. is 315 whose first term and the common r...

The sum of some terms of G.P. is 315 who | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.

Answer:

Let the sum of n terms of the G.P. be 315.

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

It is given that the first term a is 5 and common ratio r is 2.

$therefore space 315 space equals fraction numerator 5 open parentheses 2 to the power of n minus 1 close parentheses space over denominator 2 minus 1 end fraction rightwards double arrow 2 to the power of n space end exponent minus 1 space equals space 63 rightwards double arrow 2 to the power of n space equals 64 space equals space open parentheses 2 close parentheses to the power of 6 rightwards double arrow n equals 6$

∴Last term of the G.P = 6th term = ar⁶ ^{– 1} = (5)(2)⁵ = (5)(32) = 160

Thus, the last term of the G.P. is 160.

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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 5 , Question 8: The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively....

The sum of some terms of G.P. is 315 who | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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