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 :

Sum of 1 st 25 terms $=$ sum of its next 15 terms

$\Rightarrow\left(\mathrm{T}_{1}+\ldots . .+\mathrm{T}_{25}\right)=\left(\mathrm{T}_{26}+\ldots . .+\mathrm{T}_{40}\right)$

$\Rightarrow\left(\mathrm{T}_{1}+\ldots . .+\mathrm{T}_{40}\right)=2\left(\mathrm{~T}_{1}+\ldots . .+\mathrm{T}_{25}\right)$

$\Rightarrow \frac{40}{2}[2 \times 3+(39 \mathrm{~d})]=2 \times \frac{25}{2}[2 \times 2+24 \mathrm{~d}]$

$\Rightarrow \mathrm{d}=\frac{1}{6}$