In a flower decoration, the first layer has (5) flowers and each next layer has (5) more flowers. How many flowers are there in (10) layers?
Answer and explanation
Correct answer: 275
The numbers of flowers in the layers form an AP: \(5,10,15,\ldots\). Here, \(a=5\), \(d=5\), and \(n=10\). Thus, \(S_{10}=\frac{10}{2}[2(5)+(10-1)5]=5(55)=275\). Therefore, there are 275 flowers in 10 layers. The value 250 can result from an incorrect sum; in AP questions, always check the number of terms \(n\).
Frequently asked questions
What is the correct answer to this question?
275
Why is this the correct answer?
The numbers of flowers in the layers form an AP: \(5,10,15,\ldots\). Here, \(a=5\), \(d=5\), and \(n=10\). Thus, \(S_{10}=\frac{10}{2}[2(5)+(10-1)5]=5(55)=275\). Therefore, there are 275 flowers in 10 layers. The value 250 can result from an incorrect sum; in AP questions, always check the number of terms \(n\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Word problems based on APs.
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