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 :
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 :
Correct Option: , 4
Solution:
Sum of 1 st 25 terms $=$ sum of its next 15 terms
$\Rightarrow\left(\mathrm{T}_{1}+\ldots . .+\mathrm{T}_{25}\right)=\left(\mathrm{T}_{26}+\ldots . .+\mathrm{T}_{40}\right)$
$\Rightarrow\left(\mathrm{T}_{1}+\ldots . .+\mathrm{T}_{40}\right)=2\left(\mathrm{~T}_{1}+\ldots . .+\mathrm{T}_{25}\right)$
$\Rightarrow \frac{40}{2}[2 \times 3+(39 \mathrm{~d})]=2 \times \frac{25}{2}[2 \times 2+24 \mathrm{~d}]$
$\Rightarrow \mathrm{d}=\frac{1}{6}$
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