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

  • A1786
  • B843
  • C443
  • D1643

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?

  • A𝑎=𝑛(𝑛+2), where 𝑛1.
  • B𝑎=𝑛3, where 𝑛2.
  • C𝑎=3(𝑛+3), where 𝑛1.
  • D𝑎=5𝑎, 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
  • B37
  • C73
  • D13
  • 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?

  • A𝑎<1, 1<𝑟<0
  • B𝑎>0, 0<𝑟<1
  • C𝑎<0, 1<𝑟<0
  • D𝑎<0, 0<𝑟<1
  • E𝑎>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?

  • A𝑎>0, 0<𝑟<1
  • B𝑎>0, 1<𝑟<0
  • C𝑎<0, 1<𝑟<0
  • D𝑎>0, 𝑟=1
  • E𝑎>0, 𝑟<1

Q13:

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

  • A98
  • B18
  • C178
  • D89

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.

Day1st2nd3rd4th
Number of Bacteria6432,57210,28841,152
  • A83
  • B14
  • C8
  • D4
  • E3

Q15:

Which of the following is not a geometric sequence?

  • A𝑤7𝑥,16,7𝑥36𝑤,49𝑥216𝑤,
  • B(11,44,176,704,)
  • C𝑏,𝑏,𝑏,𝑏,loglogloglog
  • D119,157,1171,1513,

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,.

  • A6 or 8
  • B6 or 2
  • C6 or 2
  • D6 or2
  • E2 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 2,69210,768

  • A𝑎=43,072LE, 𝑎=10,768LE
  • B𝑎=43,072LE, 𝑎=172,288LE
  • C𝑎=172,288LE, 𝑎=689,152LE
  • D𝑎=43,072LE, 𝑎=689,152LE

Q19:

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

  • A83
  • B13,888
  • C163
  • D323

Q20:

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

Q21:

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

  • A2,10,50,250,1,250
  • B1,250,250,50,10,2
  • C10,50,250,1,250,6,250
  • D10,2,1,250,50,250

Q22:

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

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,.

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

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,.

  • A𝑎=3, 𝑟=4
  • B𝑎=8, 𝑟=4
  • C𝑎=4, 𝑟=3
  • D𝑎=2, 𝑟=3
  • E𝑎=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.

YearFirst Second Third Fourth Fifth
Salary in pounds73,600110,400165,600

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