If the sum of the first n terms of an AP is Sₙ = 4n² - 3n, find the sum of the terms from the 12th term to the 20th term, inclusive.
Answer and explanation
Correct answer: 1089
The governing concept is that the sum from the rth term to the sth term of a sequence is Sₛ - Sᵣ₋₁. Since the required terms begin with the 12th term and end with the 20th term, calculate S20 - S11. From the given expression, S20 = 4(20)² - 3(20) = 1600 - 60 = 1540. Also, S11 = 4(11)² - 3(11) = 484 - 33 = 451. Hence the required sum is 1540 - 451 = 1089. Therefore option D is correct. Subtracting S12 or S10 would exclude or include the wrong boundary term, which explains the likely distractors.
Frequently asked questions
What is the correct answer to this question?
1089
Why is this the correct answer?
The governing concept is that the sum from the rth term to the sth term of a sequence is Sₛ - Sᵣ₋₁. Since the required terms begin with the 12th term and end with the 20th term, calculate S20 - S11. From the given expression, S20 = 4(20)² - 3(20) = 1600 - 60 = 1540. Also, S11 = 4(11)² - 3(11) = 484 - 33 = 451. Hence the required sum is 1540 - 451 = 1089. Therefore option D is correct. Subtracting S12 or S10 would exclude or include the wrong boundary term, which explains the likely distractors.
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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