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Class 10MathematicsArithmetic Progressions (AP)Finding the $n$th term of an APExpertLevel 65
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In the AP (43,60,77,\ldots), what is the greatest term between (1200) and (1300)?

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Answer and explanation

Correct answer: 1284

Here, the first term is 43 and the common difference is 17. The nth term is \(a_n=43+17(n-1)\). For the greatest term less than 1300, use \(43+17(n-1)<1300\), which gives \(n\leq 74\). Therefore, \(a_{74}=43+17\times73=1284\). The number 1299 is not a term of the AP, while 1301 is greater than 1300. Exam tip: To find the largest AP term within a limit, write the nth-term formula and solve the relevant inequality.

Related tags

Arithmetic ProgressionNth TermAp RangeInequalitiesClass 10 Mathematics

Frequently asked questions

What is the correct answer to this question?

1284

Why is this the correct answer?

Here, the first term is 43 and the common difference is 17. The nth term is \(a_n=43+17(n-1)\). For the greatest term less than 1300, use \(43+17(n-1)<1300\), which gives \(n\leq 74\). Therefore, \(a_{74}=43+17\times73=1284\). The number 1299 is not a term of the AP, while 1301 is greater than 1300. Exam tip: To find the largest AP term within a limit, write the nth-term formula and solve the relevant inequality.

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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