Find the sum of the first (10) terms of the AP (30,27,24,\ldots).
Answer and explanation
Correct answer: 165
For this AP, the first term is \(a=30\), the common difference is \(d=27-30=-3\), and \(n=10\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{10}=\frac{10}{2}[2(30)+9(-3)]=5(60-27)=165\). Therefore, 165 is correct. If you get 160, recheck the common difference or the number of terms. Exam tip: always retain the negative sign of \(d\) in a decreasing AP.
Frequently asked questions
What is the correct answer to this question?
165
Why is this the correct answer?
For this AP, the first term is \(a=30\), the common difference is \(d=27-30=-3\), and \(n=10\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{10}=\frac{10}{2}[2(30)+9(-3)]=5(60-27)=165\). Therefore, 165 is correct. If you get 160, recheck the common difference or the number of terms. Exam tip: always retain the negative sign of \(d\) in a decreasing AP.
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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