Question

If $4^{th},7^{th}$ and ${10}^{th}$ terms of a $G.P.$ be $a,b,c$ respectively, thn the relation between $a,b,c$ is

• A. $b=\frac{a+c}{2}$
• B. $a^2=bc$
• C. $b^2=ac$
• D. $c^2=ab$

Answer 1

The correct option is C $b^2=ac$

Let the first element be $x$ and and the ratio be $r$

$a=x{r}^3$ (1)

$b=x{r}^6$ (2)

$c=x{r}^9$ (3)

Multiplying (1) and (3)

$ac=x^2{r}^{12}=(x{r}^6{)}^2=b^2$

Hence the correct option is (C).