What is the sum of the first (14) terms of the AP (12,17,22,\ldots)?
Answer and explanation
Correct answer: 623
Here, the first term is \(a=12\), the common difference is \(d=17-12=5\), and the number of terms is \(n=14\). Applying \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{14}=\frac{14}{2}[2(12)+13(5)]=7(89)=623\). Hence, 623 is correct. 615 is incorrect because a 14-term AP has \((n-1)=13\) common-difference intervals. Exam tip: identify \(a\), \(d\), and \(n\) before substituting in the sum formula.
Frequently asked questions
What is the correct answer to this question?
623
Why is this the correct answer?
Here, the first term is \(a=12\), the common difference is \(d=17-12=5\), and the number of terms is \(n=14\). Applying \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{14}=\frac{14}{2}[2(12)+13(5)]=7(89)=623\). Hence, 623 is correct. 615 is incorrect because a 14-term AP has \((n-1)=13\) common-difference intervals. Exam tip: identify \(a\), \(d\), and \(n\) before substituting in 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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