Worksheet: Finding the Geometric Sequence

In this worksheet, we will practice finding geometric sequences given some information about it.

Q1:

Find the geometric sequence given 𝑎+𝑎=50 and 𝑎+𝑎=125.

  • A 1 5 , 2 5 , 4 5 ,
  • B 1 5 , 2 5 , 4 5 ,
  • C ( 5 , 1 0 , 2 0 , ) or (5,10,20,)
  • D 1 5 , 2 5 , 4 5 , or 15,25,45,

Q2:

Find the geometric sequence given the common ratio is 23 and the third term is 52.

  • A 5 2 , 1 0 4 3 , 2 0 8 9 ,
  • B ( 1 1 7 , 7 8 , 5 2 , )
  • C 1 7 6 , 3 5 2 3 , 7 0 4 9 ,
  • D 1 1 7 , 3 5 1 2 , 1 , 0 5 3 4 ,

Q3:

Find the geometric sequence given 𝑎𝑎=5,832, 𝑎𝑎=2,592, and all terms are positive.

  • A ( 1 0 8 , 3 2 4 , 9 7 2 , )
  • B 8 1 3 , 2 4 1 3 , 7 2 1 3 ,
  • C ( 2 , 6 , 1 8 , )
  • D 2 , 3 2 , 9 8 ,

Q4:

Find the geometric sequence in which 𝑎𝑎=138 and 𝑎𝑎=69. Recall that 𝑎 is the 𝑛th term of a sequence.

  • A ( 2 3 , 4 6 , 9 2 , )
  • B ( 9 2 , 4 6 , 2 3 , )
  • C ( 2 3 , 4 6 , 9 2 , )
  • D ( 9 2 , 4 6 , 2 3 , )

Q5:

Find the geometric sequence in which 𝑎+𝑎=18 and 𝑎+𝑎=9.

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

Q6:

Find the geometric sequence given the sum of the first and second terms is 192, and the sum of the sixth and seventh terms is 6. Then find the order of the term whose value is 4.

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

Q7:

Find the increasing geometric sequence given the third term exceeds the sum of the first two terms by 50, and the sum of the first and third terms exceeds the second by 70.

  • A 1 0 , 3 0 , 9 0 ,
  • B 1 0 , 3 0 , 9 0 ,
  • C 1 0 , 2 0 , 4 0 ,
  • D 1 0 , 2 0 , 4 0 ,
  • E 1 0 , 2 0 , 4 0 , or 10,30,90,

Q8:

Find the geometric sequence given 𝑎+𝑎+𝑎+𝑎=85, 𝑎𝑎=510, and all terms are positive.

  • A 1 7 8 , 5 1 8 , 1 5 3 8 , or 178,174,172,
  • B 1 7 8 , 1 7 4 , 1 7 2 ,
  • C 1 7 8 , 5 1 8 , 1 5 3 8 ,
  • D 1 7 , 5 1 , 1 5 3 ,
  • E 1 7 , 3 4 , 6 8 ,

Q9:

Find the geometric sequence given that 𝑎+𝑎=6𝑎, 𝑎=78 and all terms are positive.

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

Q10:

Find the geometric sequence given the sum of the first three terms is 112 and 𝑎+𝑎+𝑎=14.

  • A 1 6 , 3 2 , 6 4 ,
  • B 1 6 , 3 2 , 6 4 ,
  • C 6 4 , 3 2 , 1 6 ,
  • D 6 4 , 3 2 , 1 6 ,

Q11:

Find the geometric sequence where 𝑎=500 and 𝑎=125.

  • A ( 5 0 0 , 2 5 0 , 1 2 5 , )
  • B ( 5 0 0 , 2 5 0 , 1 2 5 , )
  • C ( 5 0 0 , 2 5 0 , 1 2 5 , ) or (500,250,125,)
  • D 5 0 0 , 1 2 5 2 , 1 2 5
  • E 5 0 0 , 1 2 5 2 , 1 2 5 or 500,1252,125

Q12:

Find the geometric sequence in which 𝑎+𝑎=6 and 𝑎×𝑎=7.

  • A 1 7 , 1 , 7 , or 1474,214,34,
  • B ( 4 9 , 7 , 1 , ) or 17,1,7,
  • C 1 4 7 4 , 2 1 4 , 3 4 , or (3,21,147,)
  • D ( 4 9 , 7 , 1 , ) or (3,21,147,)

Q13:

Find the geometric sequence given the third term equals the multiplicative inverse of the first term and the fifth term equals 6427.

  • A 4 3 , 1 , 3 4 , or 43,1,34,
  • B 4 3 , 1 , 3 4 ,
  • C 3 4 , 1 , 4 3 , or 34,1,43,
  • D 3 4 , 1 , 4 3 , or 34,1,43,

Q14:

Find the geometric sequence 𝑎, given 7𝑎=56𝑎 and 𝑎𝑎=156.

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

Q15:

Find a geometric sequence given the second term is 6 and the sum of the first and third terms is 15.

  • A 1 2 , 6 , 3 , or 3,6,12,
  • B 3 , 6 , 1 2 , or 13,16,112,
  • C 3 , 6 , 1 2 , or 12,6,3,
  • D 1 2 , 6 , 3 , or 3,6,12,
  • E 1 2 , 6 , 3 , or 3,6,12,

Q16:

Find the geometric sequence given the sum of the second and third terms is 9 and the product of the first and fourth terms is 36.

  • A 7 2 9 8 , 8 1 8 , 9 8 , or 18,98,818,
  • B 7 2 9 1 0 , 8 1 1 0 , 9 1 0 , or 110,910,8110,
  • C 1 4 4 5 , 3 6 5 , 9 5 , or 920,95,365,
  • D ( 4 8 , 1 2 , 3 , ) or 34,3,12,

Q17:

Find the geometric sequence given 𝑎=𝑎1, 𝑎+𝑎=5 and the first term is positive.

  • A 4 , 2 , 1 , or 12,1,2,
  • B 4 , 2 , 1 ,
  • C 1 6 , 1 3 , 2 3 ,
  • D 4 3 , 2 3 , 1 3 ,
  • E 1 2 , 1 , 2 ,

Q18:

Find the geometric sequence given 𝑎=25 and 𝑎=800.

  • A ( 2 5 , 5 0 , 1 0 0 , )
  • B 2 5 , 2 5 2 , 2 5 4 ,
  • C 1 2 5 , 2 2 5 , 4 2 5 ,
  • D 1 2 5 , 1 5 0 , 1 1 0 0 ,

Q19:

Find the geometric sequence given the second and first terms add up to 187, the seventh term is four times the ninth term, and all terms are positive.

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

Q20:

Find the geometric sequence given 𝑎+𝑎=100,𝑎+𝑎=𝑎 and all terms are positive.

  • A 1 0 , 3 0 , 9 0 ,
  • B 1 0 , 3 0 , 9 0 ,
  • C 1 0 , 3 0 , 9 0 ,
  • D 1 0 , 1 0 3 , 1 0 9 ,
  • E 1 1 0 , 1 3 0 , 1 9 0 ,

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