If the sum of an AP is (S_n=7n^2-4n), find the sum from the (21)st term to the (30)th term.
Answer and explanation
Correct answer: (3460)
When a question gives the sum of the first n terms, the sum of any consecutive block can be found by subtracting the sum before that block. The terms from the 21st through the 30th are obtained by removing the first 20 terms from the first 30 terms. Thus the required expression is \\(S_{30}-S_{20}\\), not \\(S_{30}-S_{21}\\), because the 21st term must be included.
Using \\(S_n=7n^2-4n\\), we get \\(S_{30}=7(30)^2-4(30)=6180\\) and \\(S_{20}=7(20)^2-4(20)=2720\\). Therefore, the required sum is \\(6180-2720=3460\\). Option A is correct. A common mistake is to subtract \\(S_{21}\\), which would leave out the 21st term.
Frequently asked questions
What is the correct answer to this question?
(3460)
Why is this the correct answer?
When a question gives the sum of the first n terms, the sum of any consecutive block can be found by subtracting the sum before that block. The terms from the 21st through the 30th are obtained by removing the first 20 terms from the first 30 terms. Thus the required expression is \\(S_{30}-S_{20}\\), not \\(S_{30}-S_{21}\\), because the 21st term must be included.
Using \\(S_n=7n^2-4n\\), we get \\(S_{30}=7(30)^2-4(30)=6180\\) and \\(S_{20}=7(20)^2-4(20)=2720\\). Therefore, the required sum is \\(6180-2720=3460\\). Option A is correct. A common mistake is to subtract \\(S_{21}\\), which would leave out the 21st 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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