Worksheet: Geometric Sequences

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
  • C 1 3
  • D8

Q2:

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

  • A 5 1 , 0 2 4
  • B 5 , 1 2 0
  • C 1 , 2 8 0
  • D 5 2 5 6

Q3:

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

  • A 1 5 5 , 1 1 6 5 , 1 4 9 5 , 1 1 , 4 8 5
  • B 9 5 5 , 2 7 5 5 , 8 1 5 5 , 2 4 3 5 5
  • C 4 5 5 , 1 1 1 , 6 5 5 , 7 5 5
  • D 9 5 5 , 8 1 5 5 , 2 7 5 5 , 2 4 3 5 5

Q4:

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

  • A 1 7 8 6
  • B 8 4 3
  • C 4 4 3
  • D 1 6 4 3

Q5:

State whether the following is true or false: The terms of a geometric sequence can be plotted as a set of collinear points.

  • Afalse
  • Btrue

Q6:

Find the next term in the sequence 6,30,150,750,.

Q7:

Which of the following is a geometric sequence?

  • A 𝑎 = 𝑛 ( 𝑛 + 2 ) , where 𝑛1.
  • B 𝑎 = 𝑛 3 , where 𝑛2.
  • C 𝑎 = 3 ( 𝑛 + 3 ) , where 𝑛1.
  • D 𝑎 = 5 𝑎 , where 𝑛2.

Q8:

State whether the following is true or false: A geometric sequence is decreasing if its common ratio 𝑟(1,0).

  • ATrue
  • BFalse

Q9:

Find the common ratio of a geometric sequence given the middle terms are 56 and 168 respectively.

  • A112
  • B 3 7
  • C 7 3
  • D 1 3
  • E3

Q10:

State whether the following is true or false: A geometric sequence is alternating if its common ratio 𝑟 satisfies 𝑟(1,0).

  • Afalse
  • Btrue

Q11:

For an increasing geometric sequence with first term 𝑎, and common ratio 𝑟, which of the following could be true?

  • A 𝑎 < 1 , 1 < 𝑟 < 0
  • B 𝑎 > 0 , 0 < 𝑟 < 1
  • C 𝑎 < 0 , 1 < 𝑟 < 0
  • D 𝑎 < 0 , 0 < 𝑟 < 1
  • E 𝑎 > 0 , 1 < 𝑟 < 0

Q12:

A geometric sequence has a first term, 𝑎, and a common ratio, 𝑟. Which of the following conditions ensures that the sequence is NOT alternating?

  • A 𝑎 > 0 , 0 < 𝑟 < 1
  • B 𝑎 > 0 , 1 < 𝑟 < 0
  • C 𝑎 < 0 , 1 < 𝑟 < 0
  • D 𝑎 > 0 , 𝑟 = 1
  • E 𝑎 > 0 , 𝑟 < 1

Q13:

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

  • A 9 8
  • B 1 8
  • C 1 7 8
  • D 8 9

Q14:

The table shows the number of bacteria in a laboratory experiment across four consecutive days. The number of bacteria can be described by a geometric sequence. Find the common ratio of this sequence.

Day 1st 2nd 3rd 4th
Number of Bacteria 643 2,572 10,288 41,152
  • A 8 3
  • B 1 4
  • C8
  • D4
  • E3

Q15:

Which of the following is not a geometric sequence?

  • A 𝑤 7 𝑥 , 1 6 , 7 𝑥 3 6 𝑤 , 4 9 𝑥 2 1 6 𝑤 ,
  • B ( 1 1 , 4 4 , 1 7 6 , 7 0 4 , )
  • C 𝑏 , 𝑏 , 𝑏 , 𝑏 , l o g l o g l o g l o g
  • D 1 1 9 , 1 5 7 , 1 1 7 1 , 1 5 1 3 ,

Q16:

For the given sequence, what is the missing term? 60,,2,160,12,960,77,760,

Q17:

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

  • A 6 or 8
  • B6 or 2
  • C 6 or 2
  • D 6 or2
  • E 2 or 8

Q18:

The table below represents the salary of an employee in three consecutive years in LE. The salary can be described by a geometric sequence. Find the salary of the employee in the fourth and fifth year, expressed by 𝑎 and 𝑎 respectively.

Year First Second Third Fourth Fifth
Salary in LE 673 2,692 10,768

  • A 𝑎 = 4 3 , 0 7 2 L E , 𝑎 = 1 0 , 7 6 8 L E
  • B 𝑎 = 4 3 , 0 7 2 L E , 𝑎 = 1 7 2 , 2 8 8 L E
  • C 𝑎 = 1 7 2 , 2 8 8 L E , 𝑎 = 6 8 9 , 1 5 2 L E
  • D 𝑎 = 4 3 , 0 7 2 L E , 𝑎 = 6 8 9 , 1 5 2 L E

Q19:

Find the value of the second term of the geometric sequence 𝑎=16×2, where 𝑛1.

  • A 8 3
  • B 1 3 , 8 8 8
  • C 1 6 3
  • D 3 2 3

Q20:

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

  • A 𝑥 = 1 , 𝑦 = 6 4
  • B 𝑥 = 6 4 , 𝑦 = 1
  • C 𝑥 = 1 6 4 , 𝑦 = 1 4 , 0 9 6
  • D 𝑥 = 1 , 𝑦 = 4
  • E 𝑥 = 4 , 𝑦 = 1

Q21:

Find the first five terms of the sequence with general term 𝑎=5𝑎, where 𝑛1 and 𝑎=2.

  • A 2 , 1 0 , 5 0 , 2 5 0 , 1 , 2 5 0
  • B 1 , 2 5 0 , 2 5 0 , 5 0 , 1 0 , 2
  • C 1 0 , 5 0 , 2 5 0 , 1 , 2 5 0 , 6 , 2 5 0
  • D 1 0 , 2 , 1 , 2 5 0 , 5 0 , 2 5 0

Q22:

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

  • A 2 7 4 , 2 7 1 6 , 2 7 6 4 , 2 7 2 5 6 , 2 7 1 , 0 2 4
  • B 2 7 , 2 7 4 , 2 7 1 6 , 2 7 6 4 , 2 7 2 5 6
  • C 2 7 4 , 2 7 1 6 , 2 7 6 4 , 2 7 2 5 6 , 2 7 1 , 0 2 4
  • D 2 7 , 2 7 4 , 2 7 1 6 , 2 7 6 4 , 2 7 2 5 6

Q23:

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,.

  • A 𝑎 = 2 5 0 , 𝑟 = 1 5
  • B 𝑎 = 2 5 0 , 𝑟 = 5
  • C 𝑎 = 5 0 , 𝑟 = 5
  • D 𝑎 = 2 0 0 , 𝑟 = 4 5
  • E 𝑎 = 5 0 , 𝑟 = 1 0

Q24:

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: 4,12,36,108,.

  • A 𝑎 = 3 , 𝑟 = 4
  • B 𝑎 = 8 , 𝑟 = 4
  • C 𝑎 = 4 , 𝑟 = 3
  • D 𝑎 = 2 , 𝑟 = 3
  • E 𝑎 = 4 , 𝑟 = 8

Q25:

The table below represents the salary of an employee in three consecutive years. The salary can be described by a geometric sequence. Find the total salary of the employee over 5 years.

Year First Second Third Fourth Fifth
Salary in pounds 73,600 110,400 165,600

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.