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

Welcome to the NCERT Solutions for Class 11th Mathematics - Chapter Sequence and Series. This page offers a step-by-step solution to the specific question from Excercise ".$ex_no." , Question 8: the sum of some terms of g p is 315 whose first t....
Question 8

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 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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