What is the sum of the first (25) terms of the arithmetic progression (12,18,24,\ldots)?
Answer and explanation
Correct answer: 2100
Here, the first term is \(a=12\), the common difference is \(d=18-12=6\), and the number of terms is \(n=25\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{25}=\frac{25}{2}[2(12)+24\times6]=\frac{25}{2}(168)=2100\). Therefore, option C is correct. Taking \(24\) as the first term would be incorrect; it is the value of \((n-1)\). Exam tip: always check \(n-1\) carefully in the sum formula.
Frequently asked questions
What is the correct answer to this question?
2100
Why is this the correct answer?
Here, the first term is \(a=12\), the common difference is \(d=18-12=6\), and the number of terms is \(n=25\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{25}=\frac{25}{2}[2(12)+24\times6]=\frac{25}{2}(168)=2100\). Therefore, option C is correct. Taking \(24\) as the first term would be incorrect; it is the value of \((n-1)\). Exam tip: always check \(n-1\) carefully in the sum formula.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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