Find the sum of the first 22 natural numbers.
Answer and explanation
Correct answer: 253
For the first n natural numbers, the governing formula is S_n = n(n + 1)/2. Here n = 22, so S_22 = 22 × 23 / 2. Because 22 is even, divide it by 2 first: 22/2 = 11. Then multiply 11 × 23 = 253. Hence option A is correct. Another check uses the average of the first and last terms: the average is (1 + 22)/2 = 11.5, and there are 22 terms, giving 22 × 11.5 = 253. Options B, C, and D result from using an incorrect last term, omitting a term, or making an arithmetic error.
Frequently asked questions
What is the correct answer to this question?
253
Why is this the correct answer?
For the first n natural numbers, the governing formula is S_n = n(n + 1)/2. Here n = 22, so S_22 = 22 × 23 / 2. Because 22 is even, divide it by 2 first: 22/2 = 11. Then multiply 11 × 23 = 253. Hence option A is correct. Another check uses the average of the first and last terms: the average is (1 + 22)/2 = 11.5, and there are 22 terms, giving 22 × 11.5 = 253. Options B, C, and D result from using an incorrect last term, omitting a term, or making an arithmetic error.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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