If Sₙ = 7n² − 2n, find the sum from the 41st term to the 60th term.
Answer and explanation
Correct answer: 13960
Sₙ denotes the sum of the first n terms. To obtain the sum from the 41st through the 60th term, subtract the sum of the first 40 terms from the sum of the first 60 terms: required sum = S₆₀ − S₄₀. Using the given expression, S₆₀ = 7(60²) − 2(60) = 7(3600) − 120 = 25,080, and S₄₀ = 7(40²) − 2(40) = 7(1600) − 80 = 11,120. Hence the required sum is 25,080 − 11,120 = 13,960. Therefore option A is correct. Subtracting S₄₁ or S₆₀ − S₄₁ would omit the 41st term.
Frequently asked questions
What is the correct answer to this question?
13960
Why is this the correct answer?
Sₙ denotes the sum of the first n terms. To obtain the sum from the 41st through the 60th term, subtract the sum of the first 40 terms from the sum of the first 60 terms: required sum = S₆₀ − S₄₀. Using the given expression, S₆₀ = 7(60²) − 2(60) = 7(3600) − 120 = 25,080, and S₄₀ = 7(40²) − 2(40) = 7(1600) − 80 = 11,120. Hence the required sum is 25,080 − 11,120 = 13,960. Therefore option A is correct. Subtracting S₄₁ or S₆₀ − S₄₁ would omit the 41st 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.
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