GATE 2023 BT – Question 32
A series (S) is given as S = 1 + 3 + 5 + 7 + 9 + ...... The sum of the first 50 terms of S is ____________.
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Correct answer: 2500
Explanation
The series $1+3+5+7+\cdots$ is the sum of the odd numbers. It is an arithmetic progression with $a=1$ and $d=2$.
**Sum of the first $n$ terms:**
$$S_n=\frac n2\big[2a+(n-1)d\big]=\frac n2\big[2+2(n-1)\big]=n^2 .$$
For $n=50$:
$$S_{50}=50^2=\mathbf{2500}.$$