Question

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.

Answer 1

Let a be the first term and r be the common ratio of the G.P.
∴ a = –3
It is known that, an = ar^n–1
∴ a₄ = ar³ = (–3) r³
a₂ = a r¹ = (–3) r
According to the given condition,
(–3) r³ = [(–3) r]²
⇒ –3r³ = 9 r² ⇒ r = –3 a₇ = a r ^7–1 = a 

r⁶ = (–3) (–3)⁶ = – (3)⁷ = –2187
Thus, the seventh term of the G.P. is –2187.