If (S_n=5n^2-2n), find the sum from the (26)th term to the (40)th term.
Answer and explanation
Correct answer: (4845)
The notation gives the sum of the first n terms as \\(S_n=5n^2-2n\\). To add terms from the 26th through the 40th, use the total through the 40th term and remove the total through the 25th term. This works because the first 25 terms end immediately before the 26th term, so no required term is lost or counted twice.
Calculate \\(S_{40}=5(40)^2-2(40)=8000-80=7920\\). Next, \\(S_{25}=5(25)^2-2(25)=3125-50=3075\\). Therefore the required sum is \\(S_{40}-S_{25}=7920-3075=4845\\). Hence option D follows. Subtracting \\(S_{26}\\) would be wrong because the 26th term must be included.
Frequently asked questions
What is the correct answer to this question?
(4845)
Why is this the correct answer?
The notation gives the sum of the first n terms as \\(S_n=5n^2-2n\\). To add terms from the 26th through the 40th, use the total through the 40th term and remove the total through the 25th term. This works because the first 25 terms end immediately before the 26th term, so no required term is lost or counted twice.
Calculate \\(S_{40}=5(40)^2-2(40)=8000-80=7920\\). Next, \\(S_{25}=5(25)^2-2(25)=3125-50=3075\\). Therefore the required sum is \\(S_{40}-S_{25}=7920-3075=4845\\). Hence option D follows. Subtracting \\(S_{26}\\) would be wrong because the 26th term must be included.
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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