The sum of the first n terms of an arithmetic progression is S_n = n(4n − 1). What is the 20th term?
Answer and explanation
Correct answer: 155
The governing relationship between consecutive partial sums and an individual term is a_n = S_n − S_{n−1}. First evaluate S_20 using the given expression: S_20 = 20(4×20 − 1) = 20(80 − 1) = 1580. Next evaluate S_19: S_19 = 19(4×19 − 1) = 19(76 − 1) = 19×75 = 1425. Therefore, a_20 = S_20 − S_19 = 1580 − 1425 = 155. Hence option B is correct. A common mistake is to use S_20 itself as the 20th term, while the other choices can arise from an arithmetic error in one of the two evaluations.
Frequently asked questions
What is the correct answer to this question?
155
Why is this the correct answer?
The governing relationship between consecutive partial sums and an individual term is a_n = S_n − S_{n−1}. First evaluate S_20 using the given expression: S_20 = 20(4×20 − 1) = 20(80 − 1) = 1580. Next evaluate S_19: S_19 = 19(4×19 − 1) = 19(76 − 1) = 19×75 = 1425. Therefore, a_20 = S_20 − S_19 = 1580 − 1425 = 155. Hence option B is correct. A common mistake is to use S_20 itself as the 20th term, while the other choices can arise from an arithmetic error in one of the two evaluations.
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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