Question

If the fourth and seventh terms of a G.P are 10 and 80 respectively, then find the tenth term.

• A. 600
• B. 610
• C. 640
• D. 620

Answer 1

The correct option is C

640

Let the first term and the common ratio of the GP be $a$ and $r$ respectively.

Fourth term, $a_4=a{r}^3=10$

Seventh term, $a_7=a{r}^6=80$

$\Rightarrow \frac{a{r}^6}{a{r}^3}=\frac{80}{10}$

$\Rightarrow r^3=8\Rightarrow r=2$

$\therefore a_4=a{r}^3\Rightarrow a\times 8=10$

$\Rightarrow a=\frac{5}{4}$

Now, the tenth term of the GP is given by
$a_{10}=a{r}^9$

$=\frac{5}{4}\times 2^9$

$=640.$