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Class 9MathematicsSequences and ProgressionsRecursive ruleExpertLevel 44
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If (a_1=4) and (a_{n+1}=2a_n+9), what is the value of (a_4-a_2)?

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Answer and explanation

Correct answer: 78

Use the recursive rule to find the required terms: \(a_2=2(4)+9=17\), \(a_3=2(17)+9=43\), and \(a_4=2(43)+9=95\). Therefore, \(a_4-a_2=95-17=78\), so option D is correct. A common error is to stop at \(a_3\) instead of calculating the required fourth term. Exam tip: in a recursive sequence, generate terms step by step until both requested terms are obtained.

Related tags

Recursive SequencesRecurrence RelationSequence TermsTerm DifferenceClass 9 Mathematics

Frequently asked questions

What is the correct answer to this question?

78

Why is this the correct answer?

Use the recursive rule to find the required terms: \(a_2=2(4)+9=17\), \(a_3=2(17)+9=43\), and \(a_4=2(43)+9=95\). Therefore, \(a_4-a_2=95-17=78\), so option D is correct. A common error is to stop at \(a_3\) instead of calculating the required fourth term. Exam tip: in a recursive sequence, generate terms step by step until both requested terms are obtained.

Which subject and chapter does this question cover?

This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Recursive rule.

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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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