Question

sum of infinite terms of G.P is 12 and sum of their square is 45 find series

Answer 1

hello pari :-) 

as we know that sum of infinite terms of G.P is = 12 which means  a/(1-r) = > 15 

a² + a²r² + a²r^4 .............................infinite = > 45 

which means 

a²/ (1-r²)  = > 45 

a ×a / (1-r) (1+r)  = > 45 

and here a/ (1-r) = > 15 putting values we get 

a15/ (1+r)  = > 45 

we get a/(r+1) = > 3 

we get a = > 3(r+1) 

and we know that a/ (1-r)   = > 15 putting a = > 3( r+1) we get 

3(r+1)/(1-r)     =  >  15 

we get r+1 = > 5( 1 - r) 

we get r = > 2/3 

and we know that a = > 3 ( r+1) 

a= > 3( 2/3   + 1 )  

a = > 5 which means 

a + ar  + ar ^2 ................................................

putting r and a we get 

5  + 10/3   +  20/9 ................................. is our required answer 

hopes this will help you 

@ regards gopal khandelwal doing b-tech from IIT ROORKEY