Find the sum of the first n positive integers. Option 1: n/2 Option 2: (n+1)/2 Option 3: (n(n+1))/2 Option 4: ((n+1)(n+2))/2

Answer: (n(n+1))/2. Solution: Pairing the first and last terms of 1 + 2 + + n gives n/2 pairs each summing to (n+1), so the total is (n(n+1))/2. Checking n = 3: 1+2+3 = 6 = (3 x 4)/2.

Quantitative Reasoning

Number System

Easy

Find the sum of the first n positive integers.

$\dfrac{n}{2}$

$\dfrac{(n+1)}{2}$

$\dfrac{n(n+1)}{2}$

$\dfrac{(n+1)(n+2)}{2}$

✅ Correct Option: 3

Pairing the first and last terms of $1 + 2 + \dots + n$ gives $n/2$ pairs each summing to $(n+1)$ , so the total is $\dfrac{n(n+1)}{2}$ . Checking $n = 3$ : $1+2+3 = 6 = \dfrac{3 \times 4}{2}$ .

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(A) x + y is positive integer.

(B) xy is positive integer.

Choose the correct answer from the options given below:

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Choose the correct answer from the options given below:

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Solution

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