A catering service places (8) plates on the first table and (2) more plates on each next table. How many plates are placed on (10) tables?
Answer and explanation
Correct answer: 170
The plate counts form an arithmetic progression with first term \(a=8\), common difference \(d=2\), and \(n=10\) terms. Thus, \(S_{10}=\frac{10}{2}[2(8)+(10-1)\times2]=5(34)=170\). Therefore, 170 plates are placed on 10 tables. Getting 180 usually results from using an incorrect last term or number of terms. Exam tip: In AP word problems, identify \(a\), \(d\), and \(n\) before applying the formula for \(S_n\).
Frequently asked questions
What is the correct answer to this question?
170
Why is this the correct answer?
The plate counts form an arithmetic progression with first term \(a=8\), common difference \(d=2\), and \(n=10\) terms. Thus, \(S_{10}=\frac{10}{2}[2(8)+(10-1)\times2]=5(34)=170\). Therefore, 170 plates are placed on 10 tables. Getting 180 usually results from using an incorrect last term or number of terms. Exam tip: In AP word problems, identify \(a\), \(d\), and \(n\) before applying the formula for \(S_n\).
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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