If S₁₂ = 420 and S₆ = 150 for an AP, what is the sum from the 7th term to the 12th term, inclusive?
Answer and explanation
Correct answer: 270
The governing concept is the difference between two partial sums. S₁₂ is the total of terms 1 through 12, and S₆ is the total of terms 1 through 6. Subtracting S₆ from S₁₂ removes the first six terms and leaves exactly terms 7 through 12. Hence the required sum is S₁₂ - S₆ = 420 - 150 = 270. Therefore option A is correct. No common difference or individual term needs to be calculated. Options B, C and D are close numerical distractors, but each fails to equal the exact difference of the supplied partial sums. The inclusion of the 7th term is why S₆, rather than S₇, must be subtracted.
Frequently asked questions
What is the correct answer to this question?
270
Why is this the correct answer?
The governing concept is the difference between two partial sums. S₁₂ is the total of terms 1 through 12, and S₆ is the total of terms 1 through 6. Subtracting S₆ from S₁₂ removes the first six terms and leaves exactly terms 7 through 12. Hence the required sum is S₁₂ - S₆ = 420 - 150 = 270. Therefore option A is correct. No common difference or individual term needs to be calculated. Options B, C and D are close numerical distractors, but each fails to equal the exact difference of the supplied partial sums. The inclusion of the 7th term is why S₆, rather than S₇, must be subtracted.
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.
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