In the arithmetic progression (90,81,72,\ldots), which term is (9)?
Answer and explanation
Correct answer: 10th term
Here, the first term is 90 and the common difference is -9. The general term is \(a_n=90+(n-1)(-9)\). For the term 9, \(90-9(n-1)=9\), so \(n-1=9\) and \(n=10\). Therefore, 9 is the 10th term. The 9th term is 18, so that option is not correct. Exam tip: always use a negative common difference for a decreasing arithmetic progression.
Frequently asked questions
What is the correct answer to this question?
10th term
Why is this the correct answer?
Here, the first term is 90 and the common difference is -9. The general term is \(a_n=90+(n-1)(-9)\). For the term 9, \(90-9(n-1)=9\), so \(n-1=9\) and \(n=10\). Therefore, 9 is the 10th term. The 9th term is 18, so that option is not correct. Exam tip: always use a negative common difference 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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