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?

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 \(n\).