Which term of the arithmetic progression (12,18,24,\ldots) is (96)?
Answer and explanation
Correct answer: 15th term
Here, the first term is \(a=12\) and the common difference is \(d=18-12=6\). Using \(a_n=a+(n-1)d\), we get \(12+(n-1)\times6=96\). Thus, \((n-1)\times6=84\), so \(n-1=14\) and \(n=15\). Hence, 96 is the 15th term. The 14th term is \(90\), so that nearby option is incorrect. Exam tip: identify \(a\) and \(d\) first, then substitute them in \(a_n=a+(n-1)d\).
Frequently asked questions
What is the correct answer to this question?
15th term
Why is this the correct answer?
Here, the first term is \(a=12\) and the common difference is \(d=18-12=6\). Using \(a_n=a+(n-1)d\), we get \(12+(n-1)\times6=96\). Thus, \((n-1)\times6=84\), so \(n-1=14\) and \(n=15\). Hence, 96 is the 15th term. The 14th term is \(90\), so that nearby option is incorrect. Exam tip: identify \(a\) and \(d\) first, then substitute them in \(a_n=a+(n-1)d\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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