Question

If the $4^{th},{10}^{th}$ and ${16}^{th}$ terms of a GP are x, y and z respectively, then x,y,z are in :

• A. AP
• B. GP
• C. AGP
• D. HP

Answer 1

The correct option is B GP

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

According to the given condition,

$a_4=a{r}^3=x.....\left(1\right)$

$a_{10}=a{r}^9=y.....\left(2\right)$

$a_{16}=a{r}^{15}=z.....\left(3\right)$

Dividing (2) by (1), we get

$\frac{y}{x}=\frac{a{r}^9}{a{r}^3}$

$\frac{y}{x}=a^6$

Dividing (3) by (2), we get

$\frac{z}{y}=\frac{a{r}^{15}}{a{r}^9}$

$\frac{z}{y}=a^6$

$\therefore \frac{y}{x}=\frac{z}{y}$

Thus x,y,z are in G.P