Question

The sum of an infinite GP is 57, and the sum of their cubes is 9747. Find the GP.

Answer 1

Let the first term Of G.P. be a, and common ratio be r.

On cubing each term will become, 

a ³, a³r³ , …. 

∴This sum = \(\frac{a^3}{1-r^3}= 9747\)..... (2)

a=57(1-r) put this in equation 2 we get

⇒ 19(1-2r+r² ) = 1+r+r² 

⇒ 19r² -r² -38r-r+19-1 = 0 

⇒ 18r² -39r+18 = 0 

⇒ 6r² -13r+6 = 0 

⇒ (2r-3)(3r-2) = 0 

⇒ r = 2/3, 3/2 

But -1<r<1

⇒ r=2/3 

Substitute this value of r in equation 1 we get

Thus the first term of G.P. is 19, and the common ratio is 2/3