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Class 9MathematicsSequences and ProgressionsRecursive ruleMediumLevel 46
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If a₁ = 6 and aₙ₊₁ = aₙ + 4, what is a₉?

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Answer and explanation

Correct answer: 38

The governing concept is recursive evaluation of a sequence. Since 4 is added whenever we move from one term to the next, the sequence is also an arithmetic progression with first term a₁ = 6 and common difference d = 4. To reach a₉ from a₁, the rule must be applied 9 − 1 = 8 times, not nine times. Therefore, a₉ = 6 + 8(4) = 6 + 32 = 38. Listing the terms gives 6, 10, 14, 18, 22, 26, 30, 34, 38, which confirms the calculation. Thus option C is correct. Option A is a nearby earlier term, while option D can result from counting one extra step.

Related tags

Recursive-RuleArithmetic-ProgressionSequencesClass-9Recursive RuleSequences And ProgressionsMathematicsClass 9 Mcq

Frequently asked questions

What is the correct answer to this question?

38

Why is this the correct answer?

The governing concept is recursive evaluation of a sequence. Since 4 is added whenever we move from one term to the next, the sequence is also an arithmetic progression with first term a₁ = 6 and common difference d = 4. To reach a₉ from a₁, the rule must be applied 9 − 1 = 8 times, not nine times. Therefore, a₉ = 6 + 8(4) = 6 + 32 = 38. Listing the terms gives 6, 10, 14, 18, 22, 26, 30, 34, 38, which confirms the calculation. Thus option C is correct. Option A is a nearby earlier term, while option D can result from counting one extra step.

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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