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**The common difference of an A.P., the sum of whose n terms is $\mathbf{s}_{\mathbf{n}}$, is**

A. $\mathrm{S}_{\mathrm{n}}-2 \mathrm{~S}_{\mathrm{n}-1}+\mathrm{S}_{\mathrm{n}-2}$
B. $S_{n}-2 S_{n-1}-S_{n-2}$
C. $\mathrm{S}_{\mathrm{n}}-\mathrm{S}_{\mathrm{n}-2}$
D. $\mathrm{S}_{\mathrm{n}}-\mathrm{S}_{\mathrm{n}-1}$
**Answer: Option A**

## Show Answer

Solution(By Apex Team)

$\begin{array}{l}
\text { Sum of } n \text { terms }=S_{n} \\
\therefore a_{n}=S_{n}-S_{n-1} \\
\text { and } a_{n-1}=S_{n-1}-S_{n-2} \\
\therefore \text { Common difference }(d)=a_{n}-a_{n-1} \\
=\left(S_{n}-S_{n-1}\right)-\left(S_{n-1}-S_{n-2}\right) \\
S_{n}-S_{n-1}-S_{n-1}+S_{n-2} \\
=S_{n}-2 S_{n-1}+S_{n-2}
\end{array}$

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