In an arithmetic progression (S_{14}=777) and (t_{14}=96). What is the first term?
Answer and explanation
Correct answer: \(15\)
For an AP, the sum of the first \(n\) terms is \(S_n=\frac{n}{2}(a+t_n)\). Thus, \(777=\frac{14}{2}(a+96)=7(a+96)\). Hence \(a+96=111\), so \(a=15\). If \(17\) were used, the sum would be \(7(17+96)=791\), not the given sum. Exam tip: when \(S_n\) and \(t_n\) are given, use \(S_n=\frac{n}{2}(a+t_n)\) directly.
Frequently asked questions
What is the correct answer to this question?
\(15\)
Why is this the correct answer?
For an AP, the sum of the first \(n\) terms is \(S_n=\frac{n}{2}(a+t_n)\). Thus, \(777=\frac{14}{2}(a+96)=7(a+96)\). Hence \(a+96=111\), so \(a=15\). If \(17\) were used, the sum would be \(7(17+96)=791\), not the given sum. Exam tip: when \(S_n\) and \(t_n\) are given, use \(S_n=\frac{n}{2}(a+t_n)\) 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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