What is the sum of the first (25) terms of the AP (1,3,5,\ldots)?
Answer and explanation
Correct answer: 625
Here, the first term is \(a=1\), the common difference is \(d=2\), and \(n=25\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{25}=\frac{25}{2}[2+24\times2]=\frac{25}{2}\times50=625\). Choosing 600 would result from an error in finding the last term or the number of terms. Exam tip: the sum of the first \(n\) odd numbers \(1,3,5,\ldots\) is directly \(n^2\).
Frequently asked questions
What is the correct answer to this question?
625
Why is this the correct answer?
Here, the first term is \(a=1\), the common difference is \(d=2\), and \(n=25\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{25}=\frac{25}{2}[2+24\times2]=\frac{25}{2}\times50=625\). Choosing 600 would result from an error in finding the last term or the number of terms. Exam tip: the sum of the first \(n\) odd numbers \(1,3,5,\ldots\) is directly \(n^2\).
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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