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 6,72,108and.

Q2:

Find the geometric mean of (𝑎19) and (𝑎+19).

  • A𝑎19
  • B𝑎361
  • C𝑎
  • D𝑎361
  • E2𝑎

Q3:

Find 𝑦 given the geometric mean between 2 and 𝑦 is 10.

Q4:

Find the geometric means of the sequence (2,,,,4,802).

  • A16,128,1,024 or16,128,1,024
  • B14,98,686,4,802 or14,98,686,4,802
  • C16,128,1,024,8,192 or16,128,1,024,8,192
  • D14,98,686 or14,98,686

Q5:

Insert five positive geometric means between 2138 and 67219.

  • A2176,21152,21304,21608,211,216
  • B2119,4219,8419,16819,33619
  • C2176,21152,21304,21608,211,216
  • D2119,4219,8419,16819,33619

Q6:

Insert four geometric means between 14 and 256.

  • A12,1,2,4
  • B1,4,16,64
  • C1,4,16,64
  • D1,14,116,164
  • E1,14,116,164

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.

  • A39,18
  • B18,2
  • C27,6
  • D48,27

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 9𝑥 and 36𝑦.

  • A18𝑥𝑦
  • B18𝑥𝑦
  • C18𝑥𝑦
  • D18𝑥𝑦

Q13:

Find the geometric mean of 𝑥𝑦 and 𝑥𝑦𝑥+𝑦.

  • A|𝑥𝑦|
  • B||𝑥𝑦||
  • C|𝑥+𝑦|
  • D𝑥+𝑦

Q14:

The ratio 𝑥4=4𝑦, so 4 is the geometric mean of 𝑥 and 𝑦. Find the geometric mean of 𝑥+1𝑦 and 𝑦+1𝑥.

Q15:

Find the geometric mean of (𝑥+𝑦) and (𝑥𝑦).

  • A𝑥+𝑦
  • B|𝑥𝑦|
  • C|𝑥𝑦|
  • D|𝑥+𝑦|

Q16:

Find the geometric mean of 𝑥 and 9𝑥𝑦.

  • A9||𝑦||𝑥
  • B3||𝑥||𝑦
  • C9||𝑥||𝑦
  • D3||𝑦||𝑥

Q17:

Find the geometric mean of 3 and 6.

Q18:

The three sides of a right triangle are in a geometric sequence with a common ratio 𝑟<1. Find 𝑟.

  • A512
  • Bcannot be determined
  • C5+12
  • D5+12
  • E5+12

Q19:

Find the geometric mean of 16 and 4.

Q20:

Find the geometric mean of 16 and 216.

Q21:

Find the geometric mean of 29.75 and 42.84.

Q22:

Find the geometric means of the sequence (4,,,,1,024).

  • A20,100,500 or20,100,500
  • B16,64,256,1,024 or16,64,256,1,024
  • C20,100,500,2,500 or20,100,500,2,500
  • D16,64,256 or16,64,256

Q23:

Insert three positive geometric means between 1 and 8116.

  • A23,49,827
  • B32,94,278
  • C23,49,827
  • D32,94,278
  • E6,36,216

Q24:

Insert two geometric means between 29 and 6.

  • A13,12
  • B23,2
  • C23,2
  • D32,12
  • E32,12

Q25:

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

  • Ano
  • Byes

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