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Class 9MathematicsSequences and ProgressionsRecursive ruleMediumLevel 42
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In 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?

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Answer and explanation

Correct answer: 255

The governing concept is a recursive sequence: each term is calculated from the term immediately before it. The rule is next term = 2 × previous term + 1. Using the last given term, 2 × 127 + 1 = 254 + 1 = 255, so option C is correct. Options A and B result from incorrect arithmetic, while D does not follow the stated rule.

Related tags

SequencesRecursive-RuleDouble-And-AddSequences And ProgressionsMathematicsRecursive RuleClass 9 Mcq

Frequently asked questions

What is the correct answer to this question?

255

Why is this the correct answer?

The governing concept is a recursive sequence: each term is calculated from the term immediately before it. The rule is next term = 2 × previous term + 1. Using the last given term, 2 × 127 + 1 = 254 + 1 = 255, so option C is correct. Options A and B result from incorrect arithmetic, while D does not follow the stated rule.

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 (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?
  6. 6If (a_1=2) and (a_{n+1}=a_n+3), what is (a_4)?
  7. 7If (a_1=10) and (a_{n+1}=a_n-2), what is (a_5)?
  8. 8If (a_1=3) and (a_{n+1}=2a_n), what is the value of (a_4)?
  9. 9If \(a_1=64\) and \(a_{n+1}=\frac{a_n}{2}\), what is \(a_4\)?
  10. 10If (a_1=1) and (a_{n+1}=a_n+n), what is (a_5)?
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