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Question

Which term of the G.P. :

10, 53, 56,.......... is 572 ?

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Solution

First term, a = -10

Common ratio ( r ) = bevelled a subscript 2 over a subscript 1

r equals open parentheses bevelled fraction numerator fraction numerator 5 over denominator square root of 3 end fraction over denominator negative 10 space end fraction close parentheses space space equals negative fraction numerator 1 over denominator 2 square root of 3 end fraction

n t h space t e r m space equals negative 5 over 72

a r to the power of open parentheses n minus 1 close parentheses end exponent equals negative 5 over 72

negative 10 cross times open parentheses negative fraction numerator 1 over denominator 2 square root of 3 end fraction close parentheses to the power of open parentheses n minus 1 close parentheses end exponent equals negative 5 over 72

open parentheses negative fraction numerator 1 over denominator 2 square root of 3 end fraction close parentheses to the power of open parentheses n minus 1 close parentheses end exponent equals fraction numerator 1 over denominator 2 cross times 72 end fraction open parentheses negative fraction numerator 1 over denominator 2 square root of 3 end fraction close parentheses to the power of open parentheses n close parentheses end exponent equals open parentheses fraction numerator 1 over denominator 2 cross times 72 end fraction close parentheses cross times open parentheses negative fraction numerator 1 over denominator 2 square root of 3 end fraction close parentheses open parentheses negative fraction numerator 1 over denominator 2 square root of 3 end fraction close parentheses to the power of open parentheses n close parentheses end exponent equals open parentheses negative fraction numerator 1 over denominator 4 cross times 72 cross times square root of 3 end fraction close parentheses open parentheses negative fraction numerator 1 over denominator 2 square root of 3 end fraction close parentheses to the power of open parentheses n close parentheses end exponent equals open parentheses negative fraction numerator 1 over denominator 2 to the power of 5 cross times open parentheses square root of 3 close parentheses to the power of 5 end fraction close parentheses open parentheses negative fraction numerator 1 over denominator 2 square root of 3 end fraction close parentheses to the power of open parentheses n close parentheses end exponent equals open parentheses negative fraction numerator 1 over denominator 2 to the power of blank square root of 3 end fraction close parentheses to the power of 5 s o comma space n equals 5

Therefore ,

5th term in given G. P =negative 5 over 72

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