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Lesson: Finding the Recursive Formula of a Sequence

In this lesson, we will learn how to find the recursive formula of a sequence.

Worksheet • 4 Questions

Q1:

Write a recursive formula for the following sequence that is valid for 𝑛 β‰₯ 2 :

  • A π‘Ž = π‘Ž + 1 𝑛 𝑛 βˆ’ 1
  • B π‘Ž = π‘Ž βˆ’ 1 𝑛 𝑛 + 1
  • C π‘Ž = π‘Ž 𝑛 𝑛 + 1
  • D π‘Ž = π‘Ž βˆ’ 1 𝑛 𝑛 βˆ’ 1
  • E π‘Ž = π‘Ž 𝑛 𝑛 βˆ’ 1

Q2:

Using the absolute value function, write a recursive formula for the following sequence that is valid for 𝑛 β‰₯ 2 :

  • A π‘Ž = ( βˆ’ 1 ) ( | π‘Ž | + 1 ) 𝑛 𝑛 𝑛 βˆ’ 1
  • B π‘Ž = ( βˆ’ 1 ) ( | π‘Ž | + 1 ) 𝑛 𝑛 𝑛
  • C π‘Ž = ( 1 ) ( | π‘Ž | + 1 ) 𝑛 𝑛 𝑛 + 1
  • D π‘Ž = ( 1 ) ( | π‘Ž | βˆ’ 1 ) 𝑛 𝑛 𝑛 + 1
  • E π‘Ž = ( βˆ’ 1 ) ( | π‘Ž | βˆ’ 1 ) 𝑛 βˆ’ 𝑛 𝑛 βˆ’ 1

Q3:

Find a recursive formula for the sequence 4 8 6 , 1 6 2 , 5 4 , 1 8 , 6 , 2 , 2 3 .

  • A π‘Ž = ο€Ό 1 3  π‘Ž 𝑛 𝑛 βˆ’ 1
  • B π‘Ž = ο€Ό 1 3  𝑛 1 βˆ’ 𝑛
  • C π‘Ž = ο€Ό 1 2  𝑛 𝑛 βˆ’ 1
  • D π‘Ž = ο€Ό 1 2  𝑛 𝑛
  • E π‘Ž = ο€Ό 1 3  𝑛 𝑛 + 1
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