Question

The 4th term of a G.P. is square of its second term, and the first term is - 3. Find its 7th term.

Answer 1

Let r be the common ratio of the given G.P.

Then, $a_4=(a_2{)}^2$ [given]

Now, $a{r}^3=a^2{r}^2$

$\Rightarrow r=a$

$\Rightarrow r=-3$ [Putting a = - 3]

$\therefore a_7=a{r}^6$

$\Rightarrow a_7=(-3)(-3{)}^6$ [Putting a = - 3 and r = - 3]

$\Rightarrow a_7=(-3)(-729)$

$\Rightarrow a_7=-2187$

Thus, the 7th term of the G.P. is - 2187.