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Class 9MathematicsSequences and ProgressionsRecursive ruleMedium
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If (a_1=150) and (a_{n+1}=a_n-(4n+3)), what is (a_3)?

Answer and explanation

Correct answer: 132

Using the recursive rule with \(n=1\), \(a_2=150-(4\times1+3)=143\). Then, with \(n=2\), \(a_3=143-(4\times2+3)=143-11=132\). Therefore, 132 is correct. A value such as 129 can result from using an incorrect amount in the second subtraction. Exam tip: increase the value of \(n\) step by step while finding successive terms.

Related tags

Recursive SequencesSequence RuleArithmetic CalculationClass 9 MathematicsProgressionsRecursive RuleSequences And ProgressionsMathematics
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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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