What is the sum of the first 16 odd natural numbers?
Answer and explanation
Correct answer: 256
The odd natural numbers form the arithmetic progression 1, 3, 5, ..., 31, with first term 1, common difference 2, and 16 terms. The sum of the first n odd natural numbers is n². Therefore, S₁₆ = 16² = 16 × 16 = 256. The same result follows from the AP formula Sₙ = n/2[2a + (n − 1)d] = 16/2[2(1) + 15(2)] = 8 × 32 = 256. Hence option B is correct. Options A, C, and D result from arithmetic errors or from using an incorrect number of terms.
Frequently asked questions
What is the correct answer to this question?
256
Why is this the correct answer?
The odd natural numbers form the arithmetic progression 1, 3, 5, ..., 31, with first term 1, common difference 2, and 16 terms. The sum of the first n odd natural numbers is n². Therefore, S₁₆ = 16² = 16 × 16 = 256. The same result follows from the AP formula Sₙ = n/2[2a + (n − 1)d] = 16/2[2(1) + 15(2)] = 8 × 32 = 256. Hence option B is correct. Options A, C, and D result from arithmetic errors or from using an incorrect number of 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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