Let a,b and c be in G.P. with common ratio r where a≠0 and 0

# Let $a,b$ and $c$ be in G.P. with common ratio $r$ where . Ifand are the first three terms of an A.P., then the 4th term of this A.P. is:

1. A

$7a/3$

2. B

$a$

3. C

$5a$

4. D

$2a/3$

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### Solution:

Given, and  are in G.P. with common ratio $r$.

and   ……………… …(i)

Also, and $15c$ are in A.P.            [Given]

$⇒3a+15a{r}^{2}=14ar$          [Using (i)]

$\begin{array}{l}⇒15{r}^{2}-14r+3=0⇒15{r}^{2}-9r-5r+3=0\\ ⇒\left(3r-1\right)\left(5r-3\right)=0\end{array}$

or $3/5⇒r=1/3$            $\left[\because r\in \left(0,1/2\right]\right]$

The required A.P. is  $3a,7a/3,5a/3,\dots$

Hence, 4th term is

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