What will be the sum of the first (20) terms of the AP (18,21,24,\ldots)?
Answer and explanation
Correct answer: 930
Here, the first term is \(a=18\), the common difference is \(d=21-18=3\), and \(n=20\). Applying \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{20}=\frac{20}{2}[2(18)+19(3)]=10(36+57)=930\). Hence, 930 is the correct answer. Although 915 is a close distractor, it is not the sum produced by the given first term and common difference. Exam tip: the sum formula uses \(n-1\) because there are \(n-1\) gaps from the first term to the nth term.
Frequently asked questions
What is the correct answer to this question?
930
Why is this the correct answer?
Here, the first term is \(a=18\), the common difference is \(d=21-18=3\), and \(n=20\). Applying \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{20}=\frac{20}{2}[2(18)+19(3)]=10(36+57)=930\). Hence, 930 is the correct answer. Although 915 is a close distractor, it is not the sum produced by the given first term and common difference. Exam tip: the sum formula uses \(n-1\) because there are \(n-1\) gaps from the first term to the nth term.
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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