What is the sum of the first (9) terms of the AP (50,45,40,\ldots)?
Answer and explanation
Correct answer: 270
Here, the first term is \(a=50\), the common difference is \(d=-5\), and \(n=9\). The ninth term is \(a_9=a+(n-1)d=50+8(-5)=10\). Hence, \(S_9=\frac{n}{2}(a+l)=\frac{9}{2}(50+10)=270\). Therefore, 270 is the correct answer. A value such as 280 can result from using an incorrect last term or number of terms. In exams, find the \(n\)th term first to verify the sum.
Frequently asked questions
What is the correct answer to this question?
270
Why is this the correct answer?
Here, the first term is \(a=50\), the common difference is \(d=-5\), and \(n=9\). The ninth term is \(a_9=a+(n-1)d=50+8(-5)=10\). Hence, \(S_9=\frac{n}{2}(a+l)=\frac{9}{2}(50+10)=270\). Therefore, 270 is the correct answer. A value such as 280 can result from using an incorrect last term or number of terms. In exams, find the \(n\)th term first to verify the sum.
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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