Find the sum of the first (30) terms of the AP (3,6,9,\ldots).
Answer and explanation
Correct answer: 1395
For this AP, the first term is \(a=3\), the common difference is \(d=3\), and \(n=30\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{30}=\frac{30}{2}[2(3)+29(3)]=15(93)=1395\). Hence, 1395 is correct. An answer such as 1350 can result from using an incorrect last term or number of terms. Exam tip: write down \(a\), \(d\), and \(n\) before applying the sum formula.
Frequently asked questions
What is the correct answer to this question?
1395
Why is this the correct answer?
For this AP, the first term is \(a=3\), the common difference is \(d=3\), and \(n=30\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{30}=\frac{30}{2}[2(3)+29(3)]=15(93)=1395\). Hence, 1395 is correct. An answer such as 1350 can result from using an incorrect last term or number of terms. Exam tip: write down \(a\), \(d\), 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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