In the arithmetic progression (18,14,10,6,\ldots), which term is (-10)?
Answer and explanation
Correct answer: 8th term
Here, the first term is \(a=18\) and the common difference is \(d=14-18=-4\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(18+(n-1)(-4)=-10\), giving \(-4(n-1)=-28\), so \(n-1=7\) and \(n=8\). Therefore, \(-10\) is the eighth term. The closest distractor, the seventh term, is incorrect because the seventh term is \(-6\). Exam tip: In a decreasing AP, remember to use a negative common difference.
Frequently asked questions
What is the correct answer to this question?
8th term
Why is this the correct answer?
Here, the first term is \(a=18\) and the common difference is \(d=14-18=-4\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(18+(n-1)(-4)=-10\), giving \(-4(n-1)=-28\), so \(n-1=7\) and \(n=8\). Therefore, \(-10\) is the eighth term. The closest distractor, the seventh term, is incorrect because the seventh term is \(-6\). Exam tip: In a decreasing AP, remember to use a negative common difference.
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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