In an arithmetic progression, the first term is (21) and the eighteenth term is (106), what is the common difference?
Answer and explanation
Correct answer: 5
The nth-term formula of an arithmetic progression is \(a_n=a+(n-1)d\). Here, \(a=21\) and \(a_{18}=106\), so \(106=21+17d\). Thus, \(17d=85\), giving \(d=5\). If the common difference were 4, the eighteenth term would be \(21+17\times4=89\), not 106. Exam tip: from the first term to the nth term, the common difference is added \(n-1\) times, not n times.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The nth-term formula of an arithmetic progression is \(a_n=a+(n-1)d\). Here, \(a=21\) and \(a_{18}=106\), so \(106=21+17d\). Thus, \(17d=85\), giving \(d=5\). If the common difference were 4, the eighteenth term would be \(21+17\times4=89\), not 106. Exam tip: from the first term to the nth term, the common difference is added \(n-1\) times, not n times.
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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