Find the sum of the first 32 natural numbers.
Answer and explanation
Correct answer: 528
The natural numbers from 1 through 32 form an arithmetic progression with first term 1, last term 32, and 32 terms. The standard sum formula is S_n = n(n + 1)/2. Substituting n = 32 gives S_32 = 32 × 33 / 2 = 16 × 33 = 528. Therefore, option B is correct. The same result can be obtained by pairing the terms: 1 + 32 = 33, 2 + 31 = 33, and so on; there are 16 such pairs, giving 16 × 33 = 528. The other options reflect arithmetic errors in multiplication, division, or in counting the terms.
Frequently asked questions
What is the correct answer to this question?
528
Why is this the correct answer?
The natural numbers from 1 through 32 form an arithmetic progression with first term 1, last term 32, and 32 terms. The standard sum formula is S_n = n(n + 1)/2. Substituting n = 32 gives S_32 = 32 × 33 / 2 = 16 × 33 = 528. Therefore, option B is correct. The same result can be obtained by pairing the terms: 1 + 32 = 33, 2 + 31 = 33, and so on; there are 16 such pairs, giving 16 × 33 = 528. The other options reflect arithmetic errors in multiplication, division, or in counting the terms.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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