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Class 9MathematicsSequences and ProgressionsRecursive ruleExpert
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If (h_1=3) and (h_n=n h_{n-1}), what is the value of (h_4)?

Answer and explanation

Correct answer: 72

Under the recursive rule, each term is found by multiplying the previous term by its index. Thus, \(h_2=2\times3=6\), \(h_3=3\times6=18\), and \(h_4=4\times18=72\). Therefore, 72 is correct. An option such as 64 does not follow the required successive multiplications by 2, 3, and 4. Exam tip: write the steps for \(n=2,3,4\) separately to avoid using the wrong index.

Related tags

SequencesProgressionsRecursive RuleRecurrence RelationClass 9 MathematicsSequences And ProgressionsMathematicsClass 9 Mcq
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10 more MCQs
  1. 1If a₁ = 8, a₂ = 13, and each next term is the sum of the previous two terms, what is a₆?
  2. 2In the sequence \((2,3,5,8,13,\ldots)\), each term is the sum of the previous two terms. What is the eighth term?
  3. 3In the sequence \((1,2,4,7,11,\ldots)\), the added numbers are \((1,2,3,4,\ldots)\). What is the eighth term?
  4. 4In the sequence (15, 12, 7, 0, -9, ...), the differences are (-3, -5, -7, -9, ...). What will be the next term?
  5. 5In the sequence (7, 15, 31, 63, 127, ...), each next term is obtained by doubling the previous term and adding 1. What will be the next term?
  6. 6In the sequence (2, 3, 5, 9, 17, 33, ...), each next term is obtained by doubling the previous term and subtracting 1. What will be the next term?
  7. 7If (a_1=2) and (a_{n+1}=a_n+3), what is (a_4)?
  8. 8If (a_1=10) and (a_{n+1}=a_n-2), what is (a_5)?
  9. 9If (a_1=3) and (a_{n+1}=2a_n), what is the value of (a_4)?
  10. 10If \(a_1=64\) and \(a_{n+1}=\frac{a_n}{2}\), what is \(a_4\)?
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