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?

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.