Find the sum of the first 32 natural numbers.
Answer and explanation
Correct answer: 528
Direct answer: 528, so option B is correct. The first 32 natural numbers are 1, 2, 3, ..., 32. Their sum can be found with Sₙ = n(n + 1)/2, where n is the last natural number when the sequence begins at 1. Thus S₃₂ = 32×33/2 = 16×33 = 528. A second explanation uses pairing: pair the first and last terms, 1 + 32 = 33; then 2 + 31 = 33, and so on. There are 16 pairs, so the total is 16×33 = 528. Option A, 520, results from an arithmetic or formula error. Option C, 536, and option D, 544, likewise do not agree with the formula; one common mistake is using the wrong neighbouring number or forgetting the division by 2. The phrase ‘first 32 natural numbers’ starts at 1 here, so zero is not included. Memory cue: the sum 1 through n is n(n+1)/2.
Frequently asked questions
What is the correct answer to this question?
528
Why is this the correct answer?
Direct answer: 528, so option B is correct. The first 32 natural numbers are 1, 2, 3, ..., 32. Their sum can be found with Sₙ = n(n + 1)/2, where n is the last natural number when the sequence begins at 1. Thus S₃₂ = 32×33/2 = 16×33 = 528. A second explanation uses pairing: pair the first and last terms, 1 + 32 = 33; then 2 + 31 = 33, and so on. There are 16 pairs, so the total is 16×33 = 528. Option A, 520, results from an arithmetic or formula error. Option C, 536, and option D, 544, likewise do not agree with the formula; one common mistake is using the wrong neighbouring number or forgetting the division by 2. The phrase ‘first 32 natural numbers’ starts at 1 here, so zero is not included. Memory cue: the sum 1 through n is n(n+1)/2.
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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