What is the sum of the first (18) terms of the arithmetic progression (2,6,10,14,\ldots)?
Answer and explanation
Correct answer: 648
Here, the first term is \(a=2\), the common difference is \(d=4\), and \(n=18\). The 18th term is \(a_{18}=a+17d=2+17\times4=70\). Therefore, \(S_{18}=\frac{18}{2}(a+a_{18})=9(2+70)=648\). Hence, 648 is correct. An option such as 638 can result from a small error in finding the last term or multiplication. Exam tip: for the \(n\)th term, use \((n-1)d\), not \(nd\).
Frequently asked questions
What is the correct answer to this question?
648
Why is this the correct answer?
Here, the first term is \(a=2\), the common difference is \(d=4\), and \(n=18\). The 18th term is \(a_{18}=a+17d=2+17\times4=70\). Therefore, \(S_{18}=\frac{18}{2}(a+a_{18})=9(2+70)=648\). Hence, 648 is correct. An option such as 638 can result from a small error in finding the last term or multiplication. Exam tip: for the \(n\)th term, use \((n-1)d\), not \(nd\).
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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