Lesson Worksheet: Calculations with Arithmetic Sequences Mathematics • 9th Grade

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


Which of the following is an arithmetic sequence?

  • A(9,72,144,216,)
  • B(2,10,18,26,)
  • C13,110,117,124,
  • D(6,12,24,48,)
  • E𝑛,𝑛,𝑛,𝑛,


Write the next 3 terms in the arithmetic sequence 12,19,26,33,.

  • A61,68,75
  • B54,61,68
  • C47,54,61
  • D40,47,54
  • E68,75,82


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

  • Aincreasing
  • Bdecreasing


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


Find 𝑥 given three consecutive terms of an arithmetic sequence are 10𝑥, 4𝑥2, and 𝑥+8.

  • A4
  • B107
  • C32
  • D417


Write the first six terms of the sequence of negative odd numbers starting from 1.

  • A1,2,5,7,9,11
  • B1,2,3,4,5,6
  • C1,5,7,9,11,13
  • D1,3,5,7,9,11


Find the first five terms of the sequence whose general term is given by 𝑎=4𝑛+1 where 𝑛1.

  • 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)


Which of the following is an arithmetic sequence?

  • A𝑎=(8)
  • B𝑎=𝑛1
  • C𝑎=9𝑛8𝑛+1
  • D𝑎=9𝑛+1
  • E𝑎=𝑛7


Find the common difference of the arithmetic sequence given the general term 𝑎=3𝑛1.


Is the sequence 𝑎=7𝑛62 increasing or decreasing?

  • Adecreasing
  • Bincreasing

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