A G.P consists of 2n terms.if the sum of the terms occupying the odd places is S1 and that of the tems occupying the even terms is S2,then find the common ratio of the progression.

Let the G.P. be :       a , ar , ar² , ar³ , ............ ar^{2n - 1}       where 'r' is the common ratio

Given :   S1  =  a + ar² + ar⁴ + ........... + ar^{2n - 2}   =  a( (r² )ⁿ  -  1 ) / r² - 1

               S2  =  ar + ar³ + ar⁵ + ............. + ar^{2n - 1}   =  ar ( (r²)ⁿ  -  1 ) / r² - 1

Therefore : S2 / S1  =  r