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Class 9MathematicsSequences and ProgressionsRecursive ruleEasy
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If (a_1=1) and (a_{n+1}=a_n+n), what is (a_5)?

Answer and explanation

Correct answer: 11

Each new term is obtained by adding the current index n to the preceding term. Thus, a_2=1+1=2, a_3=2+2=4, a_4=4+3=7, and a_5=7+4=11. Therefore, the correct answer is 11. The value 9 can result from using an incorrect index at a step. Exam tip: when finding a_{n+1}, use the current value of n, not n+1.

Related tags

Recursive SequenceRecurrence RelationSequences And ProgressionsClass 9 MathematicsTerm CalculationRecursive RuleMathematicsClass 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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