Lesson Worksheet: Geometric Mean Mathematics • 10th Grade

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


Find the geometric mean of 16 and 4.


Find the geometric mean of 3 and 6.


Find the geometric mean of the numbers 6,72,108and.


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


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


Find the geometric mean of 9𝑥 and 36𝑦.

  • A18𝑥𝑦
  • B18𝑥𝑦
  • C18𝑥𝑦
  • D18𝑥𝑦


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


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.


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


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?

  • A14
  • B14
  • C7
  • Dcannot be determined
  • E14

This lesson includes 21 additional questions and 196 additional question variations for subscribers.

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