The number of pages in chapters of a book increases as (12,16,20,\ldots). How many pages will the (18)th chapter have?
Answer and explanation
Correct answer: 80
This is an arithmetic progression with first term \(a=12\) and common difference \(d=16-12=4\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{18}=12+(18-1)\times4=12+68=80\). Hence, the 18th chapter will have 80 pages. Option 84 would result from incorrectly using a larger increase than the actual common difference. Exam tip: Always use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
80
Why is this the correct answer?
This is an arithmetic progression with first term \(a=12\) and common difference \(d=16-12=4\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{18}=12+(18-1)\times4=12+68=80\). Hence, the 18th chapter will have 80 pages. Option 84 would result from incorrectly using a larger increase than the actual common difference. Exam tip: Always use \(n-1\), not \(n\), in the nth-term formula.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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