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Worksheet: Types of Sequences

Q1:

Sophia has 223 pennies in her piggy bank. Each week after that, she puts in another 50 pennies.

What type of sequence do the successive amounts in her piggy bank make?

  • Aneither geometric nor arithmetic
  • Bgeometric only
  • Cgeometric and arithmetic
  • Darithmetic only

List the first four terms of the sequence of the amounts starting with 223 as the first term.

  • A223, 273, 323, 373
  • B233, 203, 173, 143
  • C233, 283, 313, 343
  • D223, 173, 123, 73
  • E233, 293, 353, 413

For 𝑛 β‰₯ 1 , let 𝐴 ( 𝑛 ) be the number of pennies Sophia has after n weeks so that 𝐴 ( 0 ) = 2 2 3 . What is 𝐴 ( 4 ) ?

Is 𝐴 ( 6 ) > 5 0 0 true? If so, express it in words without referring to the function A.

  • AYes, after six weeks, Sophia had more than 500 pennies in her piggy bank.
  • BYes, after six weeks, Sophia has 500 pennies in her piggy bank.
  • CNo, before six weeks, Sophia has less than 500 pennies in her piggy bank.
  • DNo, after six weeks, Sophia had less than 500 pennies in her piggy bank.
  • EYes, before six weeks, Sophia has more than 500 pennies in her piggy bank.

Q2:

Consider the sequence βˆ’ 1 , 2 , βˆ’ 3 , 4 , βˆ’ 5 , 6 , … .

What kind of sequence is this?

  • Ageometric and arithmetic
  • Barithmetic only
  • Cgeometric only
  • Dneither geometric nor arithmetic

What are the 234th and the 1 3 7 1 st members of this sequence?

  • A234, 1 3 7 1
  • B βˆ’ 2 3 4 , βˆ’ 1 3 7 1
  • C βˆ’ 2 3 4 , 1 3 7 1
  • D 2 3 4 , βˆ’ 1 3 7 1

Using 𝑛 to represent the position of a term of this sequence, and starting at 𝑛 = 1 , write an expression to describe the sequence.

  • A 𝑛 ( βˆ’ 1 )   
  • B 𝑛 ( 1 ) 
  • C 𝑛 ( βˆ’ 1 ) 
  • D ( βˆ’ 1 ) 
  • E ( 𝑛 )  

Q3:

Consider the sequence

List the numbers at positions 5, 6, and 7.

  • A 1 0 1 1 , 1 1 1 3 , 1 3 1 5
  • B 8 9 , 1 0 1 1 , 1 1 1 2
  • C 7 1 0 , 9 1 3 , 1 1 1 6
  • D 9 1 0 , 1 1 1 2 , 1 3 1 4
  • E 1 0 9 , 1 1 1 0 , 1 2 1 1

What type of sequence is the given sequence?

  • Ageometric and arithmetic
  • Bgeometric
  • Carithmetic
  • Dneither geometric nor arithmetic

What is the number at position 13?

  • A 2 1 2 2
  • B 2 7 2 8
  • C 2 5 2 6
  • D 2 3 2 4
  • E 2 9 3 0

What is the number at position 𝑛 ?

  • A 2 𝑛 βˆ’ 1 2 𝑛
  • B 𝑛 + 1 𝑛
  • C 2 𝑛 + 1 2 𝑛
  • D 2 𝑛 2 𝑛 βˆ’ 1
  • E 𝑛 βˆ’ 1 𝑛