Question

he sum of the first two terms of a G.P is 27 whereas the sum of the second and third term is 54. Find the first term and the common ratio.​

Answer 1

`{ \tt{sum = \frac{a(r {}^(n - 1) )}{n - 1} }} \\ 27 = \frac{a(r {}^(2 - 1) )}{2 - 1} \\ { \bf{27 = ar - - - (i)}} \\ \\ 54 = \frac{a( {r}^(3 - 1) )}{3 - 1} \\ { \bf{108 = a {r}^(2) - - - (ii) }} \\ { \tt{(ii) / (i) : }} \\ r = (108)/(27) \\ { \bf{common \: ratio = 4}} \\ { \bf{first \: term = (27)/(4) }}`