What will be the sum of the first (18) terms of the AP (5,9,13,\ldots)?
Answer and explanation
Correct answer: 702
Here, the first term is \(a=5\), the common difference is \(d=4\), and \(n=18\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{18}=\frac{18}{2}[2(5)+17(4)]=9(10+68)=9\times78=702\). Hence, 702 is correct. The option 700 can result from an error in the final multiplication \(9\times78\). Exam tip: for \(n\) terms, the common difference is added \(n-1\) times, so use \((n-1)d\) in the formula.
Frequently asked questions
What is the correct answer to this question?
702
Why is this the correct answer?
Here, the first term is \(a=5\), the common difference is \(d=4\), and \(n=18\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{18}=\frac{18}{2}[2(5)+17(4)]=9(10+68)=9\times78=702\). Hence, 702 is correct. The option 700 can result from an error in the final multiplication \(9\times78\). Exam tip: for \(n\) terms, the common difference is added \(n-1\) times, so use \((n-1)d\) in the formula.
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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