What is the twelfth term of the arithmetic progression (11, 18, 25, 32, ...)?

Correct answer: 88

For an arithmetic progression, the nth term is found using \(a_n=a+(n-1)d\), where \(a\) is the first term and \(d\) is the common difference. In the given sequence, the first term is \(a=11\). The difference is \(18-11=7\), and the later differences also equal 7. We need the twelfth term, so use \(n=12\).

Substitution gives \(a_{12}=11+(12-1)7=11+11\times7=11+77=88\). Hence the twelfth term is 88, which is choice C. A common error is to multiply 12 by 7 without subtracting 1; that would count one extra difference. The first term itself uses zero differences, so the twelfth term uses exactly eleven differences.