KCET · Maths · Limits
If the sum of \(n\) terms of an AP is given by \(S_{n}=n^{2}+n\), then the common difference of the AP is
- A 4
- B 1
- C 2
- D 6
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Given sum of \(n\) terms of an AP.
\(\begin{aligned}
S_{n} &=n^{2}+n \\
a_{1} &=S_{1}=1+1=2 \\
a_{1}+a_{2} &=S_{2}=2^{2}+2=6 \\
a_{2} &=S_{2}-S_{1}=6-2=4 \\
d &=a_{2}-a_{1}=4-2=2
\end{aligned}\)
\(\begin{aligned}
S_{n} &=n^{2}+n \\
a_{1} &=S_{1}=1+1=2 \\
a_{1}+a_{2} &=S_{2}=2^{2}+2=6 \\
a_{2} &=S_{2}-S_{1}=6-2=4 \\
d &=a_{2}-a_{1}=4-2=2
\end{aligned}\)
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