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Worksheet: Identifying Arithmetic Sequences

Q1:

Which of the following is an arithmetic sequence?

  • A
  • B
  • C
  • D
  • E

Q2:

Write the next three terms of the arithmetic sequence 1 6 1 , 1 5 2 , 1 4 3 , 1 3 4 , … .

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

Q3:

Write the next three terms of the arithmetic sequence 3 . 3 , 4 . 2 , 5 . 1 , 6 , … .

  • A 6 . 9 , 7 . 8 , 9 . 6
  • B 6 . 9 , 8 . 7 , 9 . 6
  • C 7 . 8 , 8 . 7 , 9 . 6
  • D 6 . 9 , 7 . 8 , 8 . 7
  • E 7 . 8 , 8 . 7 , 1 1 . 5

Q4:

Create a five-term sequence by starting with the number 67 and subtracting 8 from each term.

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

Q5:

Find the first 5 terms of the sequence that follows the rule 9 𝑛 + 4 , where 𝑛 represents the position of a term in the sequence.

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

Q6:

Find the first five terms of the sequence whose general term is given by where .

  • A
  • B
  • C
  • D
  • E

Q7:

Following the sequence of the given figures, how many squares will there be in Figure 77?

Q8:

James can type 30 words per minute. The arithmetic sequence 3 0 , 6 0 , 9 0 , … represents the number of words he can type in each successive minute. How many words can he type in 33 minutes?

Q9:

For the next 3 years, the enrollment at a university is expected to increase by 55 students each year. If the university’s current enrollment is 589 students, determine their enrollment in each of the next 3 years.

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

Q10:

Noah started his action figure collection, where each year he buys 8 action figures. Write an algebraic expression that can be used to find the number of action figures he would have after 𝑛 years, and then determine how many action figures he would have after 24 years.

  • A 8 𝑛 , 32
  • B 8 + 𝑛 , 32
  • C 8 + 𝑛 , 192
  • D 8 𝑛 , 192
  • E 8 𝑛 + 8 , 200

Q11:

Use words and symbols to describe the value of each term as a function of its position, and then find the value of the sixteenth term in the sequence.

Position 7 8 9 10 𝑛
Value of Term 1 2 3 4 ?
  • Amultiply 6, 6 𝑛 , 96
  • Badd 6, 𝑛 + 6 , 22
  • Csubtract 1, 𝑛 βˆ’ 1 , 16
  • Dsubtract 6, 𝑛 βˆ’ 6 , 10
  • Eadd 1, 𝑛 + 1 3 , 28

Q12:

Use words and symbols to describe the value of each term as a function of its position, and then find the value of the twentieth term in the sequence.

Position 3 4 5 6 𝑛
Value of Term 1 2 3 4 ?
  • Amultiply 2, 2 𝑛 , 40
  • Badd 2, 𝑛 + 2 , 22
  • Csubtract 1, 𝑛 βˆ’ 1 , 20
  • Dsubtract 2, 𝑛 βˆ’ 2 , 18
  • Eadd 1, 𝑛 + 5 , 24

Q13:

The table shows the number of puzzles Victoria finished in a number of weeks. If she continues this pace, write an algebraic expression that can be used to determine the total number of puzzles she would finish after any given number of weeks. How many puzzles will Victoria have finished after 43 weeks?

Number of Weeks 1 2 3 4
Number of Puzzles 9 18 27 36
  • A 9 𝑛 , 52 puzzles
  • B 9 + 𝑛 , 52 puzzles
  • C 9 + 𝑛 , 387 puzzles
  • D 9 𝑛 , 387 puzzles
  • E 9 𝑛 + 9 , 396 puzzles

Q14:

Find, in terms of 𝑛 , the general term of the sequence ( βˆ’ 1 5 , 3 0 , βˆ’ 4 5 , 6 0 , … ) .

  • A ( βˆ’ 1 ) ( 𝑛 + 1 5 ) 𝑛
  • B ( βˆ’ 1 ) ( 1 5 ) 𝑛 𝑛
  • C ( βˆ’ 1 ) 𝑛 1 5 𝑛 𝑛
  • D ( βˆ’ 1 ) ( 1 5 𝑛 ) 𝑛