# if sum of four terms of GP is 60 and am between first and last term is 18. then find a and r.

jagdish singh singh
173 Points
12 years ago

Uttam Gulshan
31 Points
12 years ago

See this solution and answer me if you are satisfied.

Let the numbers be a , ar , ar^2 , ar^3 .

Now, sum=60.

=> a + ar + ar^2 +ar^3 =60.    ...........(i).

Also, a + ar^3 = 18*2 = 36.      ...........(ii).

=> a ( r + r^3 ) = 36.

=> a = 36 / ( r + r^3).

Now putting this in eq.(i) , we get 24(r^3) - 36(r^2) - 36r +24 = 0.

=> r = 1/2 , -1 , 2.

r=1 doesn't satisfy the condition.

So r=2 or r=1/2

When r=2 , a=4 , and when r=1/2 , a=32. Hence, solved.

Rishi Sharma
2 years ago
Dear Student,

Let the numbers be a , ar , ar^2 , ar^3 .
Now, sum=60.
=> a + ar + ar^2 +ar^3 =60. ...........(i).
Also, a + ar^3 = 18*2 = 36. ...........(ii).
=> a ( r + r^3 ) = 36.
=> a = 36 / ( r + r^3).
Now putting this in eq.(i) , we get 24(r^3) - 36(r^2) - 36r +24 = 0.
=> r = 1/2 , -1 , 2.
r=1 doesn't satisfy the condition.
So r=2 or r=1/2
When r=2 , a=4 , and when r=1/2 , a=32.

Thanks and Regards