The sum of the first (15) terms is (975), and the last term is (97). What is the first term?
Answer and explanation
Correct answer: 33
For an AP, the sum of the first \(n\) terms is \(S_n=\frac{n}{2}(a+l)\). Thus, \(975=\frac{15}{2}(a+97)\). This gives \(a+97=130\), so \(a=33\). If 35 were used as the first term, the sum would not be 975. Exam tip: When the last term is given, directly use \(S_n=\frac{n}{2}(a+l)\).
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
For an AP, the sum of the first \(n\) terms is \(S_n=\frac{n}{2}(a+l)\). Thus, \(975=\frac{15}{2}(a+97)\). This gives \(a+97=130\), so \(a=33\). If 35 were used as the first term, the sum would not be 975. Exam tip: When the last term is given, directly use \(S_n=\frac{n}{2}(a+l)\).
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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