What is the sum of the first (50) terms of the AP (2,4,6,\ldots)?
Answer and explanation
Correct answer: 2550
Here, the first term is \(a=2\), the common difference is \(d=2\), and the number of terms is \(n=50\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{50}=\frac{50}{2}[2\times2+49\times2]=25\times102=2550\). Therefore, 2550 is the correct answer. The value 2500 may result from taking the last term incorrectly instead of \(100\). Exam tip: identify \(a\), \(d\), and \(n\) before substituting into the sum formula.
Frequently asked questions
What is the correct answer to this question?
2550
Why is this the correct answer?
Here, the first term is \(a=2\), the common difference is \(d=2\), and the number of terms is \(n=50\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{50}=\frac{50}{2}[2\times2+49\times2]=25\times102=2550\). Therefore, 2550 is the correct answer. The value 2500 may result from taking the last term incorrectly instead of \(100\). Exam tip: identify \(a\), \(d\), and \(n\) before substituting into 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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