KCET · Maths · Binomial Theorem
\( 3+5+7+\ldots \ldots \) to \( n \) terms is
- A \( n(n+2) \)
- B \( (n-2) \)
- C \( n^{2} \)
- D \( (n+1)^{2} \)
Answer & Solution
Correct Answer
(A) \( n(n+2) \)
Step-by-step Solution
Detailed explanation
Given that, \( 3+5+7+\ldots . \mathrm{n} \) terms
It is in A.P. with first term, \( a=3 \) and common difference, \( d=2 \).
So, sum of first \( n \) terms of A.P. series is given by
\[
\begin{array}{l}
S_{n}=\frac{n}{2}[2 a+(n-1) d] \\
=\frac{n}{2}[2(3)+(n-1) 2] \\
=n(n+2)
\end{array}
\]
It is in A.P. with first term, \( a=3 \) and common difference, \( d=2 \).
So, sum of first \( n \) terms of A.P. series is given by
\[
\begin{array}{l}
S_{n}=\frac{n}{2}[2 a+(n-1) d] \\
=\frac{n}{2}[2(3)+(n-1) 2] \\
=n(n+2)
\end{array}
\]
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