Worksheet: Calculations with Arithmetic Sequences

In this worksheet, we will practice calculating the common difference, finding next terms in an arithmetic sequence, and checking if the sequence increases or decreases.


Write the next three terms of the arithmetic sequence 15.8,14.6,13.4,12.2,….

  • A9.8,8.6,7.2
  • B9.8,8.6,7.4
  • C11,9.8,7.4
  • D11,9.8,8.6
  • E11,8.6,7.4


Write the next three terms of the arithmetic sequence 161,152,143,134,….

  • A116,98,80
  • B125,116,107
  • C116,107,98
  • D125,123,122
  • E125,116,98


Write the next three terms of the arithmetic sequence 3.3,4.2,5.1,6,….

  • A6.9,7.8,9.6
  • B7.8,8.7,11.5
  • C6.9,7.8,8.7
  • D6.9,8.7,9.6
  • E7.8,8.7,9.6


Find 𝑛, given π‘Ž=4𝑛+5 and π‘Ž=237.


Find the first five terms of the sequence whose general term is given by π‘Ž=4𝑛+1 where 𝑛β‰₯1.

  • A(5,9,13,21,25)
  • B(1,5,9,13,21)
  • C(5,9,13,17,21)
  • D(1,5,9,13,17)
  • E(5,14,19,24,29)


Write the next three terms of the following sequence: 31,57,83,109,….

  • A161,187,213
  • B135,161,213
  • C135,137,138
  • D161,188,214
  • E135,161,187


If the multiples of any number are written in increasing order, do they form an arithmetic sequence?

  • Ano
  • Byes


Given that the sequence π‘Ž,π‘Ž,π‘Ž,π‘Ž,…,οŠͺ is arithmetic, which of the following statements is true?

  • Aπ‘Žπ‘Ž() is constant
  • Bπ‘Žβˆ’π‘Ž() is constant


The ending balances in Victoria’s savings account for each of the past four years form the sequence 800, 850, 900, 950. Is the sequence arithmetic?

  • Ayes
  • Bno


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

  • A67,59,51,43,35
  • B59,43,35,27,19
  • C67,43,35,27,19
  • D67,51,43,35,27
  • E59,51,43,35,27


Which of the following is an arithmetic sequence?

  • Aπ‘Ž=(βˆ’8)
  • Bπ‘Ž=π‘›βˆ’1
  • Cπ‘Ž=βˆ’9π‘›βˆ’8𝑛+1
  • Dπ‘Ž=βˆ’9𝑛+1
  • Eπ‘Ž=βˆšπ‘›βˆ’7


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.

  • A699,754,809
  • B589,699,754
  • C589,644,699
  • D644,754,809
  • E644,699,754


James can type 30 words per minute. The arithmetic sequence represents the number of words he can type in 30,60,90,… minutes. How many words can he type in 33 minutes.


Which of the following is an arithmetic sequence?

  • A(βˆ’9,72,144,216,…)
  • B(βˆ’2,βˆ’10,βˆ’18,βˆ’26,…)
  • Cο€Ό13,110,117,124,β€¦οˆ
  • D(6,βˆ’12,24,βˆ’48,…)
  • E𝑛,𝑛,𝑛,𝑛,β€¦ο…οŠ¬οŠ―οŠ§οŠ¨οŠ§οŠ«


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.

  • A8𝑛, 32
  • B8+𝑛, 192
  • C8+𝑛, 32
  • D8𝑛+8, 200
  • E8𝑛, 192


The sequence (π‘Ž) is an arithmetic sequence if π‘Žβˆ’π‘ŽοŠοŠ°οŠ§οŠ is .

  • Anot constant
  • Bconstant


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

  • A63,54,45,36,27
  • B13,31,40,49,58
  • C9,18,27,36,45
  • D13,22,31,40,49
  • E5,14,23,32,41


The common difference of an arithmetic sequence, denoted as 𝑑, is for each π‘›βˆˆβ„€οŠ°.

  • Anot constant
  • Bconstant


An arithmetic progression starting at π‘Ž and ending at 𝑙 has a common difference equal to 𝑑. What is the second term from the end?

  • Aπ‘™βˆ’2𝑑
  • B𝑙+𝑑
  • C𝑙
  • Dπ‘™βˆ’π‘‘


Is the sequence (2,βˆ’3,βˆ’8,βˆ’13,…) increasing or decreasing?

  • Aincreasing
  • Bdecreasing


Is the sequence π‘Ž=βˆ’7π‘›βˆ’62 increasing or decreasing?

  • Adecreasing
  • Bincreasing


James started working out to get healthier. He worked out for 2 minutes on the first day and increased his exercise duration by 8 minutes every day since. Find the sequence which represents his plan.

  • A10,18,26,34,42,…
  • B2,18,34,66,130,…
  • C2,10,18,26,34,…
  • D2,16,32,48,64,…


Find π‘₯ given three consecutive terms of an arithmetic sequence are βˆ’10π‘₯, βˆ’4π‘₯βˆ’2, and βˆ’π‘₯+8.

  • A4
  • B107
  • Cβˆ’32
  • Dβˆ’417


Find the values of 𝑙 and π‘š where 𝑙=π‘šβˆ’32 given the arithmetic sequence (βˆ’1,π‘š,…,𝑙,βˆ’41).

  • A𝑙=βˆ’37,π‘š=βˆ’9
  • B𝑙=βˆ’33,π‘š=βˆ’9
  • C𝑙=βˆ’37,π‘š=βˆ’5
  • D𝑙=βˆ’33,π‘š=βˆ’1
  • E𝑙=βˆ’41,π‘š=βˆ’9


Find π‘Ž, given the arithmetic sequence (7π‘Ž+14,4π‘Ž+4,3π‘Ž+4).

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