# Worksheet: Geometric Mean

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

**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
- B20, 500
- C196, 292
- D4, 92
- E100, 196

**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