The sum of the first (12) terms is (456), and the first term is (8). If the last term is (l), what is (l)?
Answer and explanation
Correct answer: 68
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Thus, \(456=\frac{12}{2}(8+l)=6(8+l)\). Hence, \(8+l=76\), so \(l=68\). If 66 were used, the sum would be 444, not 456. Exam tip: When the first and last terms are involved, use \(S_n=\frac{n}{2}(a+l)\) directly.
Frequently asked questions
What is the correct answer to this question?
68
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, \(456=\frac{12}{2}(8+l)=6(8+l)\). Hence, \(8+l=76\), so \(l=68\). If 66 were used, the sum would be 444, not 456. Exam tip: When the first and last terms are involved, use \(S_n=\frac{n}{2}(a+l)\) 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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