What is the sum of the first (12) terms of the AP (10,20,30,\ldots)?
Answer and explanation
Correct answer: 780
For this AP, the first term is \(a=10\), the common difference is \(d=10\), and \(n=12\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{12}=\frac{12}{2}[2(10)+11(10)]=6(130)=780\). Therefore, 780 is correct. A value such as 760 usually results from taking the number of terms or the last term incorrectly. Exam tip: always use \(n-1\) in the sum formula before substituting values.
Frequently asked questions
What is the correct answer to this question?
780
Why is this the correct answer?
For this AP, the first term is \(a=10\), the common difference is \(d=10\), and \(n=12\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{12}=\frac{12}{2}[2(10)+11(10)]=6(130)=780\). Therefore, 780 is correct. A value such as 760 usually results from taking the number of terms or the last term incorrectly. Exam tip: always use \(n-1\) in the sum formula before substituting values.
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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