Question

The $4^{th}$ 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, $a_n=a{r}^{n-1}$
∴ $a_4=a{r}^3=(–3)r^3$
$a_2=a{r}^1=(–3)r$
According to the given condition,
$(–3)r^3=\left[\right(–3)r{]}^2$
⇒ $–3r^3=9r^2$
⇒ $r=–3a_7=a{r}^{7–1}=a$
$r^6=(–3)(–3{)}^6=–(3{)}^7=–2187$
Thus, the seventh term of the G.P. is –2187.