Question

The $4^{th},7^{th}$ and ${10}^{th}$ term of a G.P. are $a,b,c$ respectively, then

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

Answer 1

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

Let $A$ be the first term and $r$ be the common ratio of the given G.P.
Then,
$a=A{r}^{(4-1)}=A{r}^3;b=A{r}^{(7-1)}=A{r}^6$ and $c=A{r}^{(10-1)}=A{r}^9$
$\therefore ac=\left(A{r}^3\right)\times \left(A{r}^9\right)=A^2{r}^{12}=(A{r}^6{)}^2=b^2$
Hence, $b^2=ac$.