What is the sum of the first (12) terms of the AP (13,16,19,\ldots)?
Answer and explanation
Correct answer: 354
Here, the first term is \(a=13\), the common difference is \(d=16-13=3\), and \(n=12\). The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus, \(S_{12}=\frac{12}{2}[2(13)+11(3)]=6(26+33)=6\times59=354\). Therefore, option A is correct. \(360\) can result from incorrectly using \(nd\) instead of \((n-1)d\). Exam tip: always use \(n-1\) with the common difference in the AP sum formula.
Frequently asked questions
What is the correct answer to this question?
354
Why is this the correct answer?
Here, the first term is \(a=13\), the common difference is \(d=16-13=3\), and \(n=12\). The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus, \(S_{12}=\frac{12}{2}[2(13)+11(3)]=6(26+33)=6\times59=354\). Therefore, option A is correct. \(360\) can result from incorrectly using \(nd\) instead of \((n-1)d\). Exam tip: always use \(n-1\) with the common difference in the AP 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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