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Question

Find the third term from the end of the G.P. 227, 29, 23, ..................., 162.

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Solution

first term {from last} , a = 162
common ratio, r = bevelled fraction numerator begin display style 2 over 27 end style over denominator begin display style 2 over 9 end style end fraction equals 1 third
nth term in G.P = a r to the power of open parentheses n minus 1 close parentheses end exponent
3rd term ,
equals 162 cross times open parentheses 1 third close parentheses to the power of open parentheses 3 minus 1 close parentheses end exponent equals space 162 cross times open parentheses 1 third close parentheses squared equals space 162 over 9 equals space space 18
third term = 18

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