# 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
• Bcannot be determined
• C7
• D
• E

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 in the geometric sequence .

Q5:

Find the order of the term in the geometric sequence .

Q6:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q7:

Find given three consecutive terms in a geometric sequence are .

• A
• B
• C
• D

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 . 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 Salary in LE First Second Third Fourth Fifth 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 .

Q19:

Find the number of terms of the geometric sequence .

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 , 5
• B , 5
• C , 6
• D , 6
• E , 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 .

• A , 8
• B , 8
• C , 9
• D , 9
• E , 9

Q24:

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

• A ,
• B ,
• C ,
• D ,
• E ,