If (S_n=n(4n+3)), find the sum from the (21)st term to the (35)th term.
Answer and explanation
Correct answer: (3345)
Here the sum of the first n terms is given directly by \\(S_n=n(4n+3)\\). For a range beginning with the 21st term, subtract the sum of the first 20 terms from the sum of the first 35 terms. This leaves exactly terms 21 through 35, including both endpoints.
Calculate \\(S_{35}=35[4(35)+3]=35(140+3)=35(143)=5005\\). Also, \\(S_{20}=20[4(20)+3]=20(80+3)=20(83)=1660\\). Therefore the required sum is \\(S_{35}-S_{20}=5005-1660=3345\\). Hence option D is correct. The subtraction uses 20, not 21, because the 20th term is the last term that must be excluded.
Frequently asked questions
What is the correct answer to this question?
(3345)
Why is this the correct answer?
Here the sum of the first n terms is given directly by \\(S_n=n(4n+3)\\). For a range beginning with the 21st term, subtract the sum of the first 20 terms from the sum of the first 35 terms. This leaves exactly terms 21 through 35, including both endpoints.
Calculate \\(S_{35}=35[4(35)+3]=35(140+3)=35(143)=5005\\). Also, \\(S_{20}=20[4(20)+3]=20(80+3)=20(83)=1660\\). Therefore the required sum is \\(S_{35}-S_{20}=5005-1660=3345\\). Hence option D is correct. The subtraction uses 20, not 21, because the 20th term is the last term that must be excluded.
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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