Worksheet: Recursive Formula of a Sequence

In this worksheet, we will practice finding the recursive formula of a sequence.

Q1:

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

  • A 𝑎 = 1 3 𝑛 𝑛 + 1
  • B 𝑎 = 1 2 𝑛 𝑛 1
  • C 𝑎 = 1 2 𝑛 𝑛
  • D 𝑎 = 1 3 𝑎 𝑛 𝑛 1
  • E 𝑎 = 1 3 𝑛 1 𝑛

Q2:

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

  • A 𝑎 = 𝑎 𝑛 𝑛 1
  • B 𝑎 = 𝑎 𝑛 𝑛 + 1
  • C 𝑎 = 𝑎 1 𝑛 𝑛 1
  • D 𝑎 = 𝑎 + 1 𝑛 𝑛 1
  • E 𝑎 = 𝑎 1 𝑛 𝑛 + 1

Q3:

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

  • A 𝑎 = ( 1 ) ( | 𝑎 | 1 ) 𝑛 𝑛 𝑛 1
  • B 𝑎 = ( 1 ) ( | 𝑎 | + 1 ) 𝑛 𝑛 𝑛 + 1
  • C 𝑎 = ( 1 ) ( | 𝑎 | 1 ) 𝑛 𝑛 𝑛 + 1
  • D 𝑎 = ( 1 ) ( | 𝑎 | + 1 ) 𝑛 𝑛 𝑛 1
  • E 𝑎 = ( 1 ) ( | 𝑎 | + 1 ) 𝑛 𝑛 𝑛

Q4:

Find a recursive formula for the sequence 𝑎 = 5 + 1 𝑛 𝑛 .

  • A 𝑎 = 5 𝑎 + 4 𝑛 + 1 𝑛 , 𝑎 = 6 1
  • B 𝑎 = 5 𝑎 + 4 𝑛 + 1 𝑛 , 𝑎 = 6 1
  • C 𝑎 = 5 𝑎 + 6 𝑛 + 1 𝑛 , 𝑎 = 6 1
  • D 𝑎 = 5 𝑎 4 𝑛 + 1 𝑛 , 𝑎 = 6 1
  • E 𝑎 = 5 𝑎 6 𝑛 + 1 𝑛 , 𝑎 = 6 1

Find a recursive formula for the sequence 𝑎 = 2 ( 5 ) + 1 𝑛 𝑛 .

  • A 𝑎 = 5 𝑎 4 𝑛 + 1 𝑛 , 𝑎 = 1 1 1
  • B 𝑎 = 5 𝑎 6 𝑛 + 1 𝑛 , 𝑎 = 1 1 1
  • C 𝑎 = 5 𝑎 + 4 𝑛 + 1 𝑛 , 𝑎 = 1 1 1
  • D 𝑎 = 5 𝑎 + 4 𝑛 + 1 𝑛 , 𝑎 = 1 1 1
  • E 𝑎 = 5 𝑎 + 6 𝑛 + 1 𝑛 , 𝑎 = 1 1 1

Find a recursive formula for the sequence 𝑎 = 1 3 ( 5 ) + 1 𝑛 𝑛 .

  • A 𝑎 = 5 𝑎 + 6 𝑛 + 1 𝑛 , 𝑎 = 8 3 1
  • B 𝑎 = 5 𝑎 + 4 𝑛 + 1 𝑛 , 𝑎 = 8 3 1
  • C 𝑎 = 5 𝑎 4 𝑛 + 1 𝑛 , 𝑎 = 8 3 1
  • D 𝑎 = 4 𝑎 + 5 𝑛 + 1 𝑛 , 𝑎 = 8 3 1
  • E 𝑎 = 5 𝑎 6 𝑛 + 1 𝑛 , 𝑎 = 8 3 1

Find a recursive formula for the sequence 𝑎 = 5 𝑎 + 1 𝑛 + 1 𝑛 and 𝑎 = 3 7 6 3 .

  • A 𝑎 = 3 ( 5 ) + 1 𝑛 𝑛
  • B 𝑎 = 3 . 0 8 ( 5 ) + 4 𝑛 𝑛
  • C 𝑎 = 3 ( 5 ) + 4 𝑛 𝑛
  • D 𝑎 = 3 . 0 0 8 ( 5 ) + 1 𝑛 𝑛
  • E 𝑎 = 2 . 9 3 6 ( 5 ) + 1 𝑛 𝑛

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