What is the sum of the first (8) terms of the AP (21,28,35,\ldots)?
Answer and explanation
Correct answer: 364
Here, the first term is \(a=21\), the common difference is \(d=28-21=7\), and \(n=8\). Thus, \(S_8=\frac{8}{2}[2(21)+(8-1)\times7]=4(42+49)=364\). Therefore, 364 is correct. The value 371 may result from incorrectly combining the eighth term, \(70\), with the sum; it is not the sum of the first 8 terms. Exam tip: Identify \(a\), \(d\), and \(n\), then apply \(S_n=\frac{n}{2}[2a+(n-1)d]\).
Frequently asked questions
What is the correct answer to this question?
364
Why is this the correct answer?
Here, the first term is \(a=21\), the common difference is \(d=28-21=7\), and \(n=8\). Thus, \(S_8=\frac{8}{2}[2(21)+(8-1)\times7]=4(42+49)=364\). Therefore, 364 is correct. The value 371 may result from incorrectly combining the eighth term, \(70\), with the sum; it is not the sum of the first 8 terms. Exam tip: Identify \(a\), \(d\), and \(n\), then apply \(S_n=\frac{n}{2}[2a+(n-1)d]\).
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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