What is the twelfth term of the arithmetic progression (11, 18, 25, 32, ...)?
Answer and explanation
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.
Frequently asked questions
What is the correct answer to this question?
88
Why is this the correct answer?
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.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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