If Sₙ − S₍ₙ₋₁₎ = 57, what is the value of Sₙ?
Answer and explanation
Correct answer: 1653
For Sₙ = 1 + 2 + 3 + ... + n, subtracting S₍ₙ₋₁₎ = 1 + 2 + ... + (n − 1) leaves only the final term n. Hence Sₙ − S₍ₙ₋₁₎ = n. The given difference is 57, so n = 57. Now calculate the required sum: S₅₇ = 57 × 58/2 = 57 × 29 = 1653. Therefore option B is correct. Option A is close but reflects an arithmetic error in the product or division. Options C and D correspond to using a larger index or adding an unrelated term. The important concept is that the difference of two consecutive partial sums identifies the newly included natural number.
Frequently asked questions
What is the correct answer to this question?
1653
Why is this the correct answer?
For Sₙ = 1 + 2 + 3 + ... + n, subtracting S₍ₙ₋₁₎ = 1 + 2 + ... + (n − 1) leaves only the final term n. Hence Sₙ − S₍ₙ₋₁₎ = n. The given difference is 57, so n = 57. Now calculate the required sum: S₅₇ = 57 × 58/2 = 57 × 29 = 1653. Therefore option B is correct. Option A is close but reflects an arithmetic error in the product or division. Options C and D correspond to using a larger index or adding an unrelated term. The important concept is that the difference of two consecutive partial sums identifies the newly included natural number.
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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