In the arithmetic progression (100,92,84,\ldots), which term is (20)?
Answer and explanation
Correct answer: 11th term
Here, the first term is \(a=100\) and the common difference is \(d=92-100=-8\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(20=100+(n-1)(-8)\), giving \(8(n-1)=80\) and hence \(n=11\). Therefore, 20 is the 11th term. The 10th term is 28, so it is a close but incorrect option. Exam tip: keep the common difference negative for a decreasing arithmetic progression.
Frequently asked questions
What is the correct answer to this question?
11th term
Why is this the correct answer?
Here, the first term is \(a=100\) and the common difference is \(d=92-100=-8\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(20=100+(n-1)(-8)\), giving \(8(n-1)=80\) and hence \(n=11\). Therefore, 20 is the 11th term. The 10th term is 28, so it is a close but incorrect option. Exam tip: keep the common difference negative for a decreasing arithmetic progression.
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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