The 4^th term of a G.P. is square of its second term, and the first term is – 3. Determine its 7^th term.

Given: a₄ = (a₂)² and a = –3

We know that in G.P a_n = ar^n-1

∴ a₂ = (–3) × r^2-1 = –3r(∵ a = –3)

Similarly,

a₄ = –3r³

∴ –3r³ = (-3r)² (∵ a₄ = (a₂)² )

∴ –3r³ = 9r²

⇒ r = –3

∴ r = –3

Now,

a₇ = ar^7-1

⇒ a₇ = (–3)( –3)⁶ (∵ a = –3 and r = –3)

⇒ a₇ = ( –3)⁷ = – 2187.

∴ a₇ = – 2187