Question

Find two geometric progressions having: 54 as third term and 27/32 as ninth term.

Answer 1

T9 is the 6th term after T3, so
27/32 = 54*r^6
1/64 = r^6
r = ± 1/2

I think you can do the rest.

Answer 2

Expand (1-x)^4.Hence find S if S = (1-x^3)^4 - (1-x^3)^3 + 6(1-x^3)^2 - 4(1-x^3) + 1.