Question

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

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

Answer 1

The correct option is A $\frac{1}{6}$

Given: first term $=3$
Let first term $=a$ and common difference $=d$
$\Rightarrow a=3$
Sum of $1^{st}25$ terms $=$ sum of its next $15$ terms
$\Rightarrow T_1+T_2+T_3+\cdots +T_{25}=T_{26}+T_{27}+\cdots +T_{40}$
$\Rightarrow \frac{25}{2}[2a+24d]=\frac{15}{2}[2\times (a+25d)+14d]$
$\Rightarrow 10a+120d=3[2a+64d]$
$\Rightarrow 4a=72d$
$\Rightarrow 12=72d$
$\therefore d=\frac{1}{6}$