Find the sum of the first 18 odd natural numbers.
Answer and explanation
Correct answer: 324
The governing result is that the sum of the first n odd natural numbers is n². These numbers form the arithmetic progression 1, 3, 5, ..., whose first term is 1 and common difference is 2. With n = 18, the sum is S_18 = 18² = 18 × 18 = 324. The same result follows from the AP formula: S_18 = 18/2[2(1) + 17(2)] = 9(2 + 34) = 324. Thus option A is correct. Option B is larger than the correct square, while C and D also arise from incorrect counting or substitution.
Frequently asked questions
What is the correct answer to this question?
324
Why is this the correct answer?
The governing result is that the sum of the first n odd natural numbers is n². These numbers form the arithmetic progression 1, 3, 5, ..., whose first term is 1 and common difference is 2. With n = 18, the sum is S_18 = 18² = 18 × 18 = 324. The same result follows from the AP formula: S_18 = 18/2[2(1) + 17(2)] = 9(2 + 34) = 324. Thus option A is correct. Option B is larger than the correct square, while C and D also arise from incorrect counting or substitution.
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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