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Worksheet: Finding the nth Term of a Geometric Sequence

Q1:

The first term of a geometric sequence is 2, and its third term is 7. If the common ratio is negative, what is the second term?

  • A 1 4
  • Bcannot be determined
  • C7
  • D 1 4
  • E 1 4

Q2:

Find , given the sum of the first three terms of a geometric sequence is 1 002 and the sum of , and is .

Q3:

Find , given the sum of the first three terms of a geometric sequence is 78 and the sum of , and is .

Q4:

Find the order of the term 1 6 3 9 in the geometric sequence 1 1 5 6 , 1 7 8 , 1 3 9 , .

Q5:

Find the order of the term 8 1 4 in the geometric sequence 4 , 6 , 9 , .

Q6:

Find the second and third terms of a geometric sequence given , and all terms are positive.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q7:

Find 𝑧 given three consecutive terms in a geometric sequence are 5 𝑧 , 𝑧 , 6 𝑧 + 1 a n d .

  • A 2 9 5
  • B 5 3 1
  • C 1
  • D 5 2 9

Q8:

The numbers 38 and 4 864 are terms of a geometric sequence. The ratio of the sum of the two terms after 38 in the sequence to the sum of the two terms before 4 864 in the sequence is 1 1 6 . How many terms lie between 38 and 4 864 in the sequence?

Q9:

In a geometric sequence and for a certain , we have , , and . Find the first 3 terms of the sequence and what is.

  • A , and
  • B , and
  • C , and
  • D , and
  • E , and

Q10:

In a geometric sequence and for a certain , we have , , and . Find the first 3 terms of the sequence and what is.

  • A , and
  • B , and
  • C , and
  • D , and
  • E , and

Q11:

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

  • A ,
  • B ,
  • C ,
  • D ,

Q12:

Find the value of given the of the geometric sequence is three times greater than the of the geometric sequence .

Q13:

The sum of the first and second terms of a geometric sequence is 54 and . Find the possible values of .

  • A144 or 432
  • B9 or 27
  • C or
  • D72 or

Q14:

The sum of the first and second terms of a geometric sequence is 45 and . Find the possible values of .

  • A240 or
  • B or
  • C or
  • D120 or 360

Q15:

Find the order of the term whose value is 4 374 in the geometric sequence .

Q16:

Find the order and value of the first term whose value is less than 0.0049 in the geometric sequence .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q17:

Find the order and value of the first term whose value is less than 0.0046 in the geometric sequence .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q18:

Find the number of terms of the geometric sequence 1 1 2 , 5 6 , 2 8 , , 7 4 .

Q19:

Find the number of terms of the geometric sequence 3 2 , 1 6 , 8 , , 1 4 .

Q20:

Find the second term of a geometric sequence given , and all terms are positive.

Q21:

Find the fourth term of a geometric sequence given , and all terms are positive.

Q22:

Find the geometric sequence given the first term is 3 and the fourth term is 81. Then find the order of the term whose value is 729.

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

Q23:

Find the geometric sequence given the first term is 72 and the fourth term is 9. Then find the order of the term whose value is 9 3 2 .

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

Q24:

Find the order of the first term whose value is greater than 500 in the geometric sequence .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,