Question

The sum of the first 8 terms of a G.P. is 5 times the sum of the first 4 terms; find the common ratio.​

Answer 1

Answer:

S

n

=

r−1

a(r

n

−1)

5=

S

4

S

8

5=

r

4

−1

r

8

−1

5=r

4

+1

4=r

4

4

4

=r

∴r=

4

4

Answer 2

Answer:

sum of n terms of G.P. is = {a(r^n - 1)]/(r - 1) according to question ;

[a(r^8 - 1)]/(r - 1) = 5{a(r^4 - 1)]/(r - 1) (r^4)^2-1= 5(r^4-1) r^2+2 or -2 r^2 = -2 square of any number can not

r^4+1=5

r^4 = 4

r^2 = 2

r = +2^1/2 ,or -2^1/2

be negative,hence

r = 2^1/2 or -2^1/2 (r= common ratio)