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

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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.

Q1:

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,…

Q2:

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

Q3:

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

  • Aincreasing
  • Bdecreasing

Q4:

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

Q5:

Find 𝑥 given three consecutive terms of an arithmetic sequence are −10𝑥, −4𝑥−2, and −𝑥+8.

  • A4
  • B107
  • C−32
  • D−417

Q6:

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

  • A−1,−2,−5,−7,−9,−11
  • B−1,−2,−3,−4,−5,−6
  • C−1,−5,−7,−9,−11,−13
  • D−1,−3,−5,−7,−9,−11

Q7:

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

Q8:

Which of the following is an arithmetic sequence?

  • A𝑎=(−8)
  • B𝑎=𝑛−1
  • C𝑎=−9𝑛−8𝑛+1
  • D𝑎=−9𝑛+1
  • E𝑎=√𝑛−7

Q9:

Find the common difference of the arithmetic sequence given the general term 𝑎=−3𝑛−1.

Q10:

Is the sequence 𝑎=−7𝑛−62 increasing or decreasing?

  • Adecreasing
  • Bincreasing

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