In an AP, the sum of the first (30) terms is (3000), and the (30)th term is (150). Find the first term.
Answer and explanation
Correct answer: 50
When the last term \(l\) is known, the sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Thus, \(3000=\frac{30}{2}(a+150)=15(a+150)\). Hence \(a+150=200\), so \(a=50\). If \(55\) were used, the sum would be \(15(55+150)=3075\), not the given sum. Exam tip: use \(S_n=\frac{n}{2}(a+l)\) directly when the last term is provided.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
When the last term \(l\) is known, the sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Thus, \(3000=\frac{30}{2}(a+150)=15(a+150)\). Hence \(a+150=200\), so \(a=50\). If \(55\) were used, the sum would be \(15(55+150)=3075\), not the given sum. Exam tip: use \(S_n=\frac{n}{2}(a+l)\) directly when the last term is provided.
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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