Lesson Worksheet: Geometric Sequences Mathematics

In this worksheet, we will practice calculating the common ratio, find next terms in an geometric sequence, and check if the sequence increases or decreases.


Find the common ratio of the geometric sequence 𝑎=1156,152,352,952,2752.

  • A2
  • B3
  • C13
  • D8


Find the next term of the geometric sequence 5,54,516,564,.

  • A51,024
  • B5,120
  • C1,280
  • D5256


Find the next four terms in the geometric sequence 1165,155,355,.

  • A155,1165,1495,11,485
  • B955,2755,8155,24355
  • C455,111,655,755
  • D955,8155,2755,24355


Find the common ratio of the geometric sequence which satisfies the relation 𝑎=98𝑎, where 𝑛1.

  • A98
  • B18
  • C178
  • D89


Find the first five terms of the sequence 𝑎, given 𝑎=14𝑎, 𝑛1, and 𝑎=27.

  • A274,2716,2764,27256,271,024
  • B27,274,2716,2764,27256
  • C274,2716,2764,27256,271,024
  • D27,274,2716,2764,27256


A geometric sequence is a list of terms which can be written in the form 𝑎,𝑎𝑟,𝑎𝑟,𝑎𝑟,, where 𝑎 is the first term and 𝑟 is the common ratio (the number you multiply one term by to get the next term in the sequence, 𝑟1).

Identify 𝑎 and 𝑟 in the following sequence: 250,50,10,2,.

  • A𝑎=250, 𝑟=15
  • B𝑎=250, 𝑟=5
  • C𝑎=50, 𝑟=5
  • D𝑎=200, 𝑟=45
  • E𝑎=50, 𝑟=10


Find the first five terms of the sequence whose 𝑛th term is given by 𝑎=38×15, where 𝑛1.

  • A15,125,1125,1625,13,125
  • B385,3825,38125,38625,383,125
  • C15,125,1125,1625,13,125
  • D385,3825,38125,38625,383,125


Find the fifth term of the geometric sequence 186,143,243,.

  • A1786
  • B843
  • C443
  • D1643


Find the value of 𝑚 given the geometric sequence 4,𝑚,2𝑚+3,.

  • A6 or 8
  • B6 or 2
  • C6 or 2
  • D6 or2
  • E2 or 8


Find 𝑥 and 𝑦 given the geometric sequence (1,4𝑥,4𝑦,64,).

  • A𝑥=1, 𝑦=64
  • B𝑥=64, 𝑦=1
  • C𝑥=164, 𝑦=14,096
  • D𝑥=1, 𝑦=4
  • E𝑥=4, 𝑦=1

This lesson includes 24 additional questions and 189 additional question variations for subscribers.

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