If Sₙ = 1275, what is the value of S₍ₙ₊₃₎?
Answer and explanation
Correct answer: 1431
Use Sₙ = n(n + 1)/2 for the sum of the first n natural numbers. We need to identify n from n(n + 1)/2 = 1275, or equivalently n(n + 1) = 2550. Since 50 × 51 = 2550, n = 50. Thus n + 3 = 53. Applying the same formula, S₅₃ = 53 × 54/2 = 53 × 27 = 1431. Therefore option C is correct. Option B, 1406, is S₅₂, so it results from advancing only two places; the other alternatives similarly come from using an incorrect index or arithmetic error. The original marked answer B was incorrect and has been corrected to C.
Frequently asked questions
What is the correct answer to this question?
1431
Why is this the correct answer?
Use Sₙ = n(n + 1)/2 for the sum of the first n natural numbers. We need to identify n from n(n + 1)/2 = 1275, or equivalently n(n + 1) = 2550. Since 50 × 51 = 2550, n = 50. Thus n + 3 = 53. Applying the same formula, S₅₃ = 53 × 54/2 = 53 × 27 = 1431. Therefore option C is correct. Option B, 1406, is S₅₂, so it results from advancing only two places; the other alternatives similarly come from using an incorrect index or arithmetic error. The original marked answer B was incorrect and has been corrected to C.
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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