# Worksheet: Finding the nth Term of a Geometric Sequence

In this worksheet, we will practice writing explicit and recursive formulas for geometric sequences to find the value of the nth term in a geometric sequence and how to find a term’s order given its value.

Q1:

Find the first three terms of a geometric sequence given and the common ratio is .

• A
• B
• C
• D
• E

Q2:

Find the value of in a geometric sequence given and all terms are positive.

• A
• B
• C
• D
• E

Q3:

Find the three consecutive numbers of a geometric sequence, given that the sum of the terms is and the product is 216.

• A, 6,
• B, ,
• C, ,
• D6, , 54
• E6, ,

Q4:

Find the three consecutive numbers of a geometric sequence, given their sum is 7 and the product of their squares is 64.

• A, , 1
• B2, 1,
• C4, 2, 1
• D, 1, 2
• E2, 4, 8

Q5:

Find the first three terms of the geometric sequence given their sum is and the sum of their squares is 21.

• A,,
• B,,
• C,,
• D,,

Q6:

Find the order of the term in the geometric sequence .

Q7:

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

• A,
• B,
• C,
• D,
• E,

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:

Find, in terms of , the general term of the sequence where .

• A
• B
• C
• D

Q11:

Determine and that make the following a geometric sequence, starting at , of the form :

• A,
• B,
• C,
• D,
• E,

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 .

• A or
• B144 or 432
• C72 or
• D9 or 27

Q14:

Find, in terms of , the general term of the sequence .

• A
• B
• C
• D

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:

Suppose that and belong to a geometric sequence with a positive . Using four decimal places for your common ratio, determine this first term to two decimal places.

• A
• B
• C
• D
• E

Q18:

Find the number of terms of the geometric sequence .

Q19:

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

Q20:

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

Q21:

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, 6
• B, 5
• C, 5
• D, 6
• E, 6

Q22:

What is the order of the term in the geometric sequence whose value is 1,572,864?

Q23:

Find, in terms of , the general term of the sequence .

• A
• B
• C
• D

Q24:

Find the geometric sequence given and the common ratio is 4.

• A
• B
• C
• D
• E

Q25:

Determine and that make a geometric sequence, starting at , of the form .

• A,
• B,
• C,
• D,
• E,