If S₁₅ = 465 and S₁₀ = 240 for an AP, what is the sum from the 11th term to the 15th term, inclusive?
Answer and explanation
Correct answer: 225
The governing concept is subtraction of partial sums. S₁₅ represents the sum of the first 15 terms, while S₁₀ represents the sum of the first 10 terms. When the latter is subtracted from the former, the first 10 terms cancel and only terms 11 through 15 remain. Therefore, required sum = S₁₅ - S₁₀ = 465 - 240 = 225. Option D is correct. This method does not require finding the first term or the common difference. A, B and C are distractors produced by incorrect subtraction or by counting the block incorrectly. Because the question includes both boundary terms, subtracting S₁₀ is exactly appropriate; subtracting S₁₁, for example, would omit the 11th term.
Frequently asked questions
What is the correct answer to this question?
225
Why is this the correct answer?
The governing concept is subtraction of partial sums. S₁₅ represents the sum of the first 15 terms, while S₁₀ represents the sum of the first 10 terms. When the latter is subtracted from the former, the first 10 terms cancel and only terms 11 through 15 remain. Therefore, required sum = S₁₅ - S₁₀ = 465 - 240 = 225. Option D is correct. This method does not require finding the first term or the common difference. A, B and C are distractors produced by incorrect subtraction or by counting the block incorrectly. Because the question includes both boundary terms, subtracting S₁₀ is exactly appropriate; subtracting S₁₁, for example, would omit the 11th term.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
