What is the sum of the first (6) terms of the AP (100,90,80,\ldots)?
Answer and explanation
Correct answer: 450
Here, the first term is \(a=100\), the common difference is \(d=-10\), and \(n=6\). The sixth term is \(a_6=a+5d=100+5(-10)=50\). Hence, \(S_6=\frac{n}{2}(a+l)=\frac{6}{2}(100+50)=450\). Therefore, 450 is correct. An answer such as 440 can result from an error in finding the last term or adding the terms. Exam tip: for a decreasing AP, the common difference \(d\) is negative.
Frequently asked questions
What is the correct answer to this question?
450
Why is this the correct answer?
Here, the first term is \(a=100\), the common difference is \(d=-10\), and \(n=6\). The sixth term is \(a_6=a+5d=100+5(-10)=50\). Hence, \(S_6=\frac{n}{2}(a+l)=\frac{6}{2}(100+50)=450\). Therefore, 450 is correct. An answer such as 440 can result from an error in finding the last term or adding the terms. Exam tip: for a decreasing AP, the common difference \(d\) is negative.
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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