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Class 9MathematicsSequences and ProgressionsRecursive ruleMedium
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If \(a_1=30\) and \(a_{n+1}=a_n-\frac{n}{2}\), what is \(a_4\)?

Answer and explanation

Correct answer: 27

In the recursive rule, use \(n=1,2,3\) successively to reach the fourth term. Thus, \(a_2=30-\frac12\), \(a_3=30-\frac12-1\), and \(a_4=30-\frac12-1-\frac32=30-3=27\). Therefore, 27 is correct. The value 26 would result from adding the subtractions incorrectly. Exam tip: to find \(a_4\) from \(a_1\), apply the rule three times.

Related tags

Recursive SequencesRecursive RuleSequence TermsFractionsClass 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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