A catering service places (10) plates on the first table and (2) more plates on each next table. How many plates are placed on (12) tables?
Answer and explanation
Correct answer: 252
The plate counts 10, 12, 14, … form an arithmetic progression with a=10, d=2, and n=12. Hence, \(S_{12}=\frac{12}{2}[2(10)+(12-1)(2)] = 6(42)=252\). Therefore, 252 plates are placed on 12 tables. The value 264 can result from using the number of terms or the last term incorrectly. Exam tip: In AP word problems, first identify a, d, and n, then apply the formula for \(S_n\).
Frequently asked questions
What is the correct answer to this question?
252
Why is this the correct answer?
The plate counts 10, 12, 14, … form an arithmetic progression with a=10, d=2, and n=12. Hence, \(S_{12}=\frac{12}{2}[2(10)+(12-1)(2)] = 6(42)=252\). Therefore, 252 plates are placed on 12 tables. The value 264 can result from using the number of terms or the last term incorrectly. Exam tip: In AP word problems, first identify a, d, and n, then apply 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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