A library has (32) books on the first shelf and each next shelf has (4) more books. How many books will be on the (25)th shelf?
Answer and explanation
Correct answer: 128
This is an arithmetic progression with first term \(a=32\), common difference \(d=4\), and \(n=25\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{25}=32+(25-1)\times4=32+96=128\). Hence, 128 is correct. Adding 4 twenty-five times would give 132, but the increase occurs only 24 times after the first shelf. Exam tip: always use \((n-1)\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
128
Why is this the correct answer?
This is an arithmetic progression with first term \(a=32\), common difference \(d=4\), and \(n=25\). The \(n\)th term is \(a_n=a+(n-1)d\). Therefore, \(a_{25}=32+(25-1)\times4=32+96=128\). Hence, 128 is correct. Adding 4 twenty-five times would give 132, but the increase occurs only 24 times after the first shelf. 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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