Question

In a G.p the ratio between the sum of first three terms and that of the first six terms is 125:152 find its common ration given

Answer 1

Let 'a' be first term and 'r' common ratio of G.P

S₃ ÷ S₆ = 125 / 152

a ( r³ - 1 ) / ( r - 1 ) ÷ a ( r ⁶ - 1) / ( r- 1) = 125 / 152

( r³ - 1 ) / ( r ⁶ - 1 ) = 125 / 152

[ r³ - 1 ] / [ (r³) ² - (1)² ] = 125 / 152

[ r³ - 1 ] / [ ( r³ - 1) (r³ + 1 ) = 125 / 152

1 / [ r³ + 1 ] = 125 / 152

152 = 125 [ r³ + 1 ]

152 =125 r³ + 125

27 / 125 = r ³

( 3/5)³ = r ³

r= 3 / 5