In an arithmetic progression the first term is (13) and the common difference is (7). What is the sum of the first (22) terms?
Answer and explanation
Correct answer: 1903
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Here, \(a=13\), \(d=7\), and \(n=22\). Thus, \(S_{22}=\frac{22}{2}[2(13)+21(7)]=11(26+147)=11\times173=1903\). Therefore, 1903 is correct. The option 1892 can result from an error in evaluating the expression inside the bracket. Exam tip: use \(n-1=21\), not 22, while finding the last term contribution.
Frequently asked questions
What is the correct answer to this question?
1903
Why is this the correct answer?
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Here, \(a=13\), \(d=7\), and \(n=22\). Thus, \(S_{22}=\frac{22}{2}[2(13)+21(7)]=11(26+147)=11\times173=1903\). Therefore, 1903 is correct. The option 1892 can result from an error in evaluating the expression inside the bracket. Exam tip: use \(n-1=21\), not 22, while finding the last term contribution.
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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