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.