Find the sum of the first (14) terms of the arithmetic progression (6,9,12,\ldots).
Answer and explanation
Correct answer: 357
Here, the first term is \(a=6\), the common difference is \(d=9-6=3\), and the number of terms is \(n=14\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{14}=\frac{14}{2}[2(6)+13(3)]=7(51)=357\). Hence, 357 is correct. An option such as 367 usually results from an error while calculating \((n-1)d\) or adding the terms. Exam tip: write down \(a\), \(d\), and \(n\) separately before applying the sum formula.
Frequently asked questions
What is the correct answer to this question?
357
Why is this the correct answer?
Here, the first term is \(a=6\), the common difference is \(d=9-6=3\), and the number of terms is \(n=14\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{14}=\frac{14}{2}[2(6)+13(3)]=7(51)=357\). Hence, 357 is correct. An option such as 367 usually results from an error while calculating \((n-1)d\) or adding the terms. Exam tip: write down \(a\), \(d\), and \(n\) separately 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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