# 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 .

• A2
• B3
• C
• D8

Q2:

Find the next term of the geometric sequence .

• A
• B
• C
• D

Q3:

Find the next four terms in the geometric sequence .

• A
• B
• C
• D

Q4:

Find the fifth term of the geometric sequence .

• A
• B
• C
• D

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 .

Q7:

Which of the following is a geometric sequence?

• A , where .
• B , where .
• C , where .
• D , where .

Q8:

State whether the following is true or false: A geometric sequence is decreasing if its common ratio .

• ATrue
• BFalse

Q9:

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

• A112
• B
• C
• D
• E3

Q10:

State whether the following is true or false: A geometric sequence is alternating if its common ratio satisfies .

• Afalse
• Btrue

Q11:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q12:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q13:

Find the common ratio of the geometric sequence which satisfies the relation , where .

• A
• B
• C
• D

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

Q15:

Which of the following is not a geometric sequence?

• A
• B
• C
• D

Q16:

For the given sequence, what is the missing term?

Q17:

Find the value of given the geometric sequence .

• A or 8
• B6 or
• C or 2
• D or
• E 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 and respectively.

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

• A ,
• B ,
• C ,
• D ,

Q19:

Find the value of the second term of the geometric sequence , where .

• A
• B
• C
• D

Q20:

Find and given the geometric sequence .

• A ,
• B ,
• C ,
• D ,
• E ,

Q21:

Find the first five terms of the sequence with general term , where and .

• A
• B
• C
• D

Q22:

Find the first five terms of the sequence , given , , and .

• A
• B
• C
• D

Q23:

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

Identify and in the following sequence: .

• A ,
• B ,
• C ,
• D ,
• E ,

Q24:

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

Identify and in the following sequence: .

• A ,
• B ,
• C ,
• D ,
• E ,

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