Question

In an $A.P$ $(p+1{)}^{th}$ term is twice the $(q+1{)}^{th}$ terms. If its $(3p+1{)}^{th}$ term is $\lambda$ times the $(p+q+1{)}^{th}$ term, then $\lambda$ is equal to:

• A. $2$
• B. $\frac{1}{2}$
• C. $3$
• D. $noneofthese$

Answer 1

The correct option is A $2$

Given that:

$p+1=2(q+1)$

On adding $2p$ both side, we get

$2p+p+1=2q+2+2p$

$3p+1=2(p+q+1)$ ......(1)

Now, according to second condition-

$3p+1=\lambda (q+1+p)$ ......(2)

On comparing equation (1) and (2), we get

$\lambda =2.$