# Worksheet: Geometric Mean

In this worksheet, we will practice finding geometric means between two nonconsecutive terms of a geometric sequence.

Q1:

Find the geometric mean of the numbers .

Q2:

Find the geometric mean of and .

• A
• B
• C
• D
• E

Q3:

Find given the geometric mean between 2 and is 10.

Q4:

Find the geometric means of the sequence .

• A or
• B or
• C or
• D or

Q5:

Insert five positive geometric means between and .

• A
• B
• C
• D

Q6:

Insert four geometric means between and 256.

• A
• B
• C
• D
• E

Q7:

Find the number of geometric means inserted between 82 and 1,312 given the sum of the last two means equals twice the sum of the first two means.

Q8:

How many geometric means are inserted between 81 and 16 so that the product of the second mean and the last mean is 864?

Q9:

Find the two positive numbers whose positive geometric mean is greater than the smaller number by 16 and less than the larger number by 80.

• A4, 100
• B196, 292
• C100, 196
• D4, 92
• E20, 500

Q10:

Find two positive numbers given their geometric mean is 36 and their difference is 21.

• A
• B
• C
• D

Q11:

Find two positive numbers given the geometric mean is 42 and the sum is 85.

• A2, 21
• B2, 83
• C36, 49
• D49, 134
• E36, 121

Q12:

Find the geometric mean of and .

• A
• B
• C
• D

Q13:

Find the geometric mean of and .

• A
• B
• C
• D

Q14:

The ratio , so 4 is the geometric mean of and . Find the geometric mean of and .

Q15:

Find the geometric mean of and .

• A
• B
• C
• D

Q16:

Find the geometric mean of and .

• A
• B
• C
• D

Q17:

Find the geometric mean of and .

Q18:

The three sides of a right triangle are in a geometric sequence with a common ratio . Find .

• A
• Bcannot be determined
• C
• D
• E

Q19:

Find the geometric mean of 16 and 4.

Q20:

Find the geometric mean of and 216.

Q21:

Find the geometric mean of 29.75 and 42.84.

Q22:

Find the geometric means of the sequence .

• A or
• B or
• C or
• D or

Q23:

Insert three positive geometric means between 1 and .

• A
• B
• C
• D
• E

Q24:

Insert two geometric means between and 6.

• A
• B
• C
• D
• E

Q25:

Is the arithmetic mean of two positive, different real numbers greater than their geometric mean?

• Ano
• Byes