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.

Q1:

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

  • A2
  • B3
  • C13
  • D8

Q2:

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

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

Q3:

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

Q4:

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

  • A98
  • B18
  • C178
  • D89

Q5:

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

Q6:

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

Q7:

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

Q8:

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

  • A1786
  • B843
  • C443
  • D1643

Q9:

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

Q10:

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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