What is the sum of the first (14) terms of the AP (4,10,16,\ldots)?
Answer and explanation
Correct answer: 602
Here, the first term is \(a=4\), the common difference is \(d=10-4=6\), and \(n=14\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{14}=\frac{14}{2}[2(4)+13(6)]=7(86)=602\). Therefore, 602 is correct. Although 604 is close, it does not result from correct substitution in the formula. Exam tip: identify \(a\), \(d\), and \(n\) before applying the sum formula.
Frequently asked questions
What is the correct answer to this question?
602
Why is this the correct answer?
Here, the first term is \(a=4\), the common difference is \(d=10-4=6\), and \(n=14\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{14}=\frac{14}{2}[2(4)+13(6)]=7(86)=602\). Therefore, 602 is correct. Although 604 is close, it does not result from correct substitution in the formula. Exam tip: identify \(a\), \(d\), and \(n\) before applying the sum formula.
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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