GATE 2020 BT – Question 5
General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice
Find the difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers.
- $n^2-n$
- $n^2+n$
- $2n^2-n$
- $2n^2+n$
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Show answer and explanation
Correct answer: (B) $n^2+n$
Explanation
The first sum is $(2n)(2n+1)/2=n(2n+1)$. The sum of the first n odd numbers is $n^2$. Subtracting gives $2n^2+n-n^2=n^2+n$, option B.
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