If Sₙ = 1953, what is the value of S₍ₙ₊₂₎?
Answer and explanation
Correct answer: 2080
First identify n using Sₙ = n(n + 1)/2. We need n(n + 1)/2 = 1953, so n(n + 1) = 3906. Since 62 × 63 = 3906, n = 62. The requested index is therefore n + 2 = 64. Applying the sum formula gives S₆₄ = 64 × 65/2 = 32 × 65 = 2080. Hence option B is correct. Option A may result from adding only one new term incorrectly, while options C and D usually arise from advancing too far or making an arithmetic error. The essential step is to recover the original index before evaluating the shifted partial sum; the symbol n is not itself equal to 1953.
Frequently asked questions
What is the correct answer to this question?
2080
Why is this the correct answer?
First identify n using Sₙ = n(n + 1)/2. We need n(n + 1)/2 = 1953, so n(n + 1) = 3906. Since 62 × 63 = 3906, n = 62. The requested index is therefore n + 2 = 64. Applying the sum formula gives S₆₄ = 64 × 65/2 = 32 × 65 = 2080. Hence option B is correct. Option A may result from adding only one new term incorrectly, while options C and D usually arise from advancing too far or making an arithmetic error. The essential step is to recover the original index before evaluating the shifted partial sum; the symbol n is not itself equal to 1953.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
