In an AP, (d=9), (n=20), and (S_{20}=2450). Find the first term (a).
Answer and explanation
Correct answer: 37
The sum of the first n terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus, \(2450=\frac{20}{2}[2a+19\times9]\), so \(2450=10(2a+171)\). Hence \(245=2a+171\), giving \(2a=74\) and \(a=37\). If 39 is used, the sum becomes greater, so it is a close but incorrect distractor. Exam tip: remember to use \((n-1)d\), which is \(19d\) when \(n=20\).
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
The sum of the first n terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus, \(2450=\frac{20}{2}[2a+19\times9]\), so \(2450=10(2a+171)\). Hence \(245=2a+171\), giving \(2a=74\) and \(a=37\). If 39 is used, the sum becomes greater, so it is a close but incorrect distractor. Exam tip: remember to use \((n-1)d\), which is \(19d\) when \(n=20\).
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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