Question

The sum of 3 terms of a G.P. is 21/4 and their product is 1 then the common ratio is ​

Answer 1

assume, first term=a and ratio=r

hence we will assume the 3 terms to be-

a/r , a , ar

therefore, product=a.a.a.r/r=a^3

∴a^3=1

a=1

a/r+a+ar=21/4

(a+ar+ar^2)/r=21/4

(r^2+r+1)4=21r

4r^2-17r+4=0

Putting this in the quadratic equation formula gives-

r=4 or r=1/4

PS- 4 or 1/4 won't make any difference here because if we assume, r=4, then the terms will be- 1/4, 1, 4

And if we assume r=1/4, then the terms will be- 4, 1, 1/4