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Class 9MathematicsSequences and ProgressionsExplicit or general ruleHardLevel 50
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Which statement about (74) is correct for the sequence (11,18,25,32,\ldots)?

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Answer and explanation

Correct answer: (74) is the tenth term

This is an arithmetic progression with first term 11 and common difference 7. Its general term is \(a_n=11+(n-1)\times7=7n+4\). Setting \(7n+4=74\) gives \(n=10\), so 74 is the tenth term. The ninth term is \(7(9)+4=67\), not 74. Exam tip: To find the position of a number in an AP, equate it to \(a_n\) and solve for \(n\).

Related tags

Arithmetic ProgressionSequenceGeneral TermNth TermLinear Sequence

Frequently asked questions

What is the correct answer to this question?

(74) is the tenth term

Why is this the correct answer?

This is an arithmetic progression with first term 11 and common difference 7. Its general term is \(a_n=11+(n-1)\times7=7n+4\). Setting \(7n+4=74\) gives \(n=10\), so 74 is the tenth term. The ninth term is \(7(9)+4=67\), not 74. Exam tip: To find the position of a number in an AP, equate it to \(a_n\) and solve for \(n\).

Which subject and chapter does this question cover?

This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.

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  1. 1For the sequence 2, 5, 10, 17, 26, ..., the nth term is a_n = n² + 1. What is the value of a_12 − a_10?
  2. 2For the sequence 6, 14, 26, 42, ..., a_n = 2n² + 2n + 2. What is the value of a_15 - a_13?
  3. 3If a_n = (-1)^n(n + 1), what will be the value of a_7 + a_8?
  4. 4What will be the next term in the sequence (1, 2, 6, 24, 120, …)?
  5. 5If a_n = 5n + (−1)^n, what will be the value of a_10 − a_9?
  6. 6If a_n = 4n^2 + 2n - 3, what will be the value of a_11?
  7. 7If a_n = (-1)^(n+1)(2n+3), what will be the value of a_8 + a_9?
  8. 8If a_n = n^2 + 6n + 5, which term is 252?
  9. 9What is the general term of the sequence (3, 6, 9, 12, …)?
  10. 10Which explicit rule is correct for the sequence (5, 10, 15, 20, …)?
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