The first term of a GP is -3 and the square of the second term is equal to its 4^th term. Find its 7^th term.

It is given that the first term of GP is -3.

So, a = -3

It is also given that the square of the second term is equal to its 4^th term.

∴ (a₂)² = a₄

n^th term of GP, a_n = ar^n-1

So, a₂ = ar; a_{4 =} ar³

(ar) ² = ar³→ a = r = -3

Now, the 7^th term in the GP, a₇ = ar⁶

a₇ = (-3)⁷ = -2187

Hence, the 7^th term of GP is -2187.