In an arithmetic progression, the first term is (31), the last term is (13), and the number of terms is (7). What is the sum?
Answer and explanation
Correct answer: 154
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, \(S_7=\frac{7}{2}(31+13)=\frac{7}{2}\times44=154\). Therefore, 154 is correct. Since the first term is greater than the last term, the AP may be decreasing, but this does not change the sum formula. 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?
154
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, \(S_7=\frac{7}{2}(31+13)=\frac{7}{2}\times44=154\). Therefore, 154 is correct. Since the first term is greater than the last term, the AP may be decreasing, but this does not change the sum formula. 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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