If (S_n=n(5n-2)), find the sum from the (16)th term to the (25)th term.
Answer and explanation
Correct answer: (1980)
The notation gives the sum of the first n terms as \\(S_n=n(5n-2)\\). To add the terms from the 16th through the 25th, subtract the sum through the 15th term from the sum through the 25th term. First, \\(S_{25}=25(5\times25-2)=25(123)=3075\\). Next, \\(S_{15}=15(5\times15-2)=15(73)=1095\\). Thus the required sum is \\(S_{25}-S_{15}=3075-1095=1980\\).
Hence option D is correct. Subtracting \\(S_{15}\\), rather than \\(S_{16}\\), is necessary because the 16th term is the first term wanted. The difference removes terms 1 through 15 and leaves exactly terms 16 through 25. The calculated value agrees with the supplied answer, so no correction is needed.
Frequently asked questions
What is the correct answer to this question?
(1980)
Why is this the correct answer?
The notation gives the sum of the first n terms as \\(S_n=n(5n-2)\\). To add the terms from the 16th through the 25th, subtract the sum through the 15th term from the sum through the 25th term. First, \\(S_{25}=25(5\times25-2)=25(123)=3075\\). Next, \\(S_{15}=15(5\times15-2)=15(73)=1095\\). Thus the required sum is \\(S_{25}-S_{15}=3075-1095=1980\\).
Hence option D is correct. Subtracting \\(S_{15}\\), rather than \\(S_{16}\\), is necessary because the 16th term is the first term wanted. The difference removes terms 1 through 15 and leaves exactly terms 16 through 25. The calculated value agrees with the supplied answer, so no correction is needed.
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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