What is the sum of the first (25) terms of the arithmetic progression (8,12,16,\ldots)?
Answer and explanation
Correct answer: 1400
Here, the first term is \(a=8\), the common difference is \(d=12-8=4\), and \(n=25\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{25}=\frac{25}{2}[2(8)+24(4)]=\frac{25}{2}(112)=1400\). Therefore, 1400 is correct. An option such as 1350 may result from an error in finding the last term or in using \((n-1)\). Exam tip: for \(n\) terms, always use \((n-1)\) with the common difference in the sum formula.
Frequently asked questions
What is the correct answer to this question?
1400
Why is this the correct answer?
Here, the first term is \(a=8\), the common difference is \(d=12-8=4\), and \(n=25\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{25}=\frac{25}{2}[2(8)+24(4)]=\frac{25}{2}(112)=1400\). Therefore, 1400 is correct. An option such as 1350 may result from an error in finding the last term or in using \((n-1)\). Exam tip: for \(n\) terms, always use \((n-1)\) with the common difference 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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