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

Let a be the first term and r be the common ratio of the G.P.

∴ a = -3

It is known that, an = \(arn^-1\)

∴\(a^4\) = a\(r^3\)= (-3) \(r^3\)

\(a^2\) = a \(r^1\)= (-3) r

According to the given condition,

(-3) \(r^3\) = [(-3) r\(]^2\)

⇒ -3\(r^3\)= 9 \(r^2\)

⇒ r = -3

\(a^7\) = a\(r^7-1\)

= a \(r^6\)

= (-3) (-3\()^6\) 

= - (3\()^7\) 

= -2187

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