Question

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

Answer 1

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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 r = (–3) r

According to the given condition,

(–3) r³ = [­(–3) r]2

⇒ r = –3

a₇ =

$ar {}^{7 - 1}$

= a r⁶= (–3) (–3)⁶ = – (3)⁷ = –2187

Thus, the seventh term of the G.P. is –2187.