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Class 9MathematicsSequences and ProgressionsRecursive ruleHard
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If (a_1=4), (a_2=8), and (a_n=a_{n-1}+a_{n-2}+6), what is (a_5)?

Answer and explanation

Correct answer: 56

The recursive rule says that each new term is obtained by adding the previous two terms and 6. Thus, a_3=4+8+6=18, a_4=8+18+6=32, and a_5=18+32+6=56. Therefore, 56 is correct. A value such as 54 results from an error in using the previous terms or adding 6. Exam tip: write each intermediate term in order when solving a recursive sequence.

Related tags

Recursive SequencesRecursive RuleSequences And ProgressionsClass 9 MathematicsNumber PatternsMathematicsClass 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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