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Subjects
Class 10MathematicsArithmetic Progressions (AP)Finding the $n$th term of an APMediumLevel 65
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The first term of an AP is (25) and the (18)th term is (93). What is the common difference?

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Answer and explanation

Correct answer: 4

For an AP, the nth-term formula is \(a_n=a+(n-1)d\). Here, \(93=25+(18-1)d\), so \(93=25+17d\). Thus, \(68=17d\) and \(d=4\). If the common difference were 3, the 18th term would be \(25+17\times3=76\), not 93. Exam tip: use \(n-1\), not n, in the nth-term formula.

Related tags

Arithmetic ProgressionCommon DifferenceNth TermClass 10 MathematicsAp Formula

Frequently asked questions

What is the correct answer to this question?

4

Why is this the correct answer?

For an AP, the nth-term formula is \(a_n=a+(n-1)d\). Here, \(93=25+(18-1)d\), so \(93=25+17d\). Thus, \(68=17d\) and \(d=4\). If the common difference were 3, the 18th term would be \(25+17\times3=76\), not 93. Exam tip: use \(n-1\), not n, in the nth-term formula.

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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10 more MCQs
  1. 1What is the fourth term in (14,18,22,26,\ldots)?
  2. 2What will be the fifth term in (2,7,12,17,\ldots)?
  3. 3What is the fourth term in the sequence (6,12,18,24,\ldots)?
  4. 4What is the third term in the sequence (9,7,5,3,\ldots)?
  5. 5A plant grows (2) cm every day. The heights are (12,14,16,18,\ldots). What is the height on the fourth day?
  6. 6In an AP, first term (a=4) and common difference (d=3). What is the (10)th term?
  7. 7Find the (12)th term of the AP (7,11,15,19,\ldots).
  8. 8What is the (9)th term of the AP (20,17,14,11,\ldots)?
  9. 9If (a=2), (d=5), what will be the (15)th term of the AP?
  10. 10Which is the (20)th term of the AP (3,8,13,18,\ldots)?
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