A catering service places (6) plates on the first table and (3) more plates on each next table. How many plates are placed on (8) tables?
Answer and explanation
Correct answer: (132)
The plate counts form an arithmetic progression: 6, 9, 12, \ldots. Here, the first term is \(a=6\), the common difference is \(d=3\), and the number of terms is \(n=8\). Thus, \(S_8=\frac{8}{2}[2(6)+(8-1)(3)]=4(12+21)=132\). Therefore, (132) is correct. A value such as (128) can result from using an incorrect common difference or number of terms. Exam tip: In AP word problems, identify \(a\), \(d\), and \(n\) before applying the sum formula.
Frequently asked questions
What is the correct answer to this question?
(132)
Why is this the correct answer?
The plate counts form an arithmetic progression: 6, 9, 12, \ldots. Here, the first term is \(a=6\), the common difference is \(d=3\), and the number of terms is \(n=8\). Thus, \(S_8=\frac{8}{2}[2(6)+(8-1)(3)]=4(12+21)=132\). Therefore, (132) is correct. A value such as (128) can result from using an incorrect common difference or number of terms. Exam tip: In AP word problems, identify \(a\), \(d\), and \(n\) before applying the sum formula.
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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