Question

If the first term of an $A.P$. is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms, then the common difference of this $A.P$. is:

• A. $\frac{1}{4}$
• B. $\frac{1}{5}$
• C. $\frac{1}{7}$
• D. $\frac{1}{6}$

Answer 1

Answer: (D)

Sum of 1 st 25 terms $=$ sum of its next 15 terms
$\Rightarrow \left(T_1+\dots \dots +T_{25}\right)=\left(T_{26}+\dots ..+T_{40}\right)$
$\Rightarrow \left(T_1+\dots ..+T_{40}\right)=2\left(T_1+\dots \dots +T_{25}\right)$
$\Rightarrow \frac{40}{2}[2\times 3+(39d)]=2\times \frac{25}{2}[2\times 2+24d]$
$\Rightarrow d=\frac{1}{6}$