What is the sum of the first (12) terms of the arithmetic progression (9,16,23,\ldots)?
Answer and explanation
Correct answer: 570
Here, the first term is \(a=9\), the common difference is \(d=16-9=7\), and \(n=12\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{12}=\frac{12}{2}[2(9)+11(7)]=6(18+77)=570\). Therefore, 570 is correct. A value such as 558 may result from using the wrong number of terms or misusing \((n-1)\). Exam tip: write down \(a\), \(d\), and \(n\) before substituting in the sum formula.
Frequently asked questions
What is the correct answer to this question?
570
Why is this the correct answer?
Here, the first term is \(a=9\), the common difference is \(d=16-9=7\), and \(n=12\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{12}=\frac{12}{2}[2(9)+11(7)]=6(18+77)=570\). Therefore, 570 is correct. A value such as 558 may result from using the wrong number of terms or misusing \((n-1)\). Exam tip: write down \(a\), \(d\), and \(n\) before substituting 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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