If the first term of an AP is (22) and (a_{32}=177), what is the common difference?
Answer and explanation
Correct answer: 5
For an AP, \(a_n=a+(n-1)d\). Here, \(a=22\), \(n=32\), and \(a_{32}=177\). Thus, \(177=22+31d\), so \(31d=155\) and \(d=5\). If the common difference were 4, the 32nd term would be \(22+31\times4=146\), not 177. Exam tip: the common difference is added \(n-1\) times to obtain the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
For an AP, \(a_n=a+(n-1)d\). Here, \(a=22\), \(n=32\), and \(a_{32}=177\). Thus, \(177=22+31d\), so \(31d=155\) and \(d=5\). If the common difference were 4, the 32nd term would be \(22+31\times4=146\), not 177. Exam tip: the common difference is added \(n-1\) times to obtain the \(n\)th term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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