If an AP has (S_{12}=390) and (d=5), what is the first term (a)?
Answer and explanation
Correct answer: 5
The sum of the first n terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus, \(390=\frac{12}{2}[2a+11\times5]=6(2a+55)\). Hence \(2a+55=65\), so \(2a=10\) and \(a=5\). If 4 were used as the first term, the sum would be 378, so it is not correct. Exam tip: In the sum formula, use \((n-1)d\), not \(nd\).
Frequently asked questions
What is the correct answer to this question?
5
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, \(390=\frac{12}{2}[2a+11\times5]=6(2a+55)\). Hence \(2a+55=65\), so \(2a=10\) and \(a=5\). If 4 were used as the first term, the sum would be 378, so it is not correct. Exam tip: In the sum formula, use \((n-1)d\), not \(nd\).
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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