If the sum of the first (10) terms of an arithmetic progression is (310), and the last term is (49), what is the first term?
Answer and explanation
Correct answer: \(13\)
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Thus, \(310=\frac{10}{2}(a+49)=5(a+49)\). Hence \(a+49=62\), so \(a=13\). If \(a=12\), the sum would be \(305\), not \(310\). Exam tip: when the last term is given, apply \(S_n=\frac{n}{2}(a+l)\) directly.
Frequently asked questions
What is the correct answer to this question?
\(13\)
Why is this the correct answer?
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Thus, \(310=\frac{10}{2}(a+49)=5(a+49)\). Hence \(a+49=62\), so \(a=13\). If \(a=12\), the sum would be \(305\), not \(310\). Exam tip: when the last term is given, apply \(S_n=\frac{n}{2}(a+l)\) directly.
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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