If the first term of an arithmetic progression is (85), the last term is (0), and the number of terms is (18), what is the sum?
Answer and explanation
Correct answer: 765
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\), where \(a\) is the first term and \(l\) is the last term. Thus, \(S_{18}=\frac{18}{2}(85+0)=9\times85=765\). Therefore, 765 is correct. A last term of 0 must still be included in the formula; it should not be omitted. Exam tip: When the first term, last term, and number of terms are given, use \(S_n=\frac{n}{2}(a+l)\) directly.
Frequently asked questions
What is the correct answer to this question?
765
Why is this the correct answer?
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\), where \(a\) is the first term and \(l\) is the last term. Thus, \(S_{18}=\frac{18}{2}(85+0)=9\times85=765\). Therefore, 765 is correct. A last term of 0 must still be included in the formula; it should not be omitted. Exam tip: When the first term, last term, and number of terms are given, 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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