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Homework Help

Lesson: Geometric Mean

In this lesson, we will learn how to find geometric means between two nonconsecutive terms of a geometric sequence.

Sample Question Videos

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Worksheet • 24 Questions • 3 Videos

Q1:

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

Q2:

The ratio π‘₯ ∢ 4 = 4 ∢ 𝑦 , so 4 is the geometric mean of π‘₯ and 𝑦 . Find the geometric mean of ο€½ π‘₯ + 1 𝑦  and ο€Ό 𝑦 + 1 π‘₯  .

Q3:

Find the geometric mean of ( π‘Ž βˆ’ 1 9 ) and ( π‘Ž + 1 9 ) .

  • A √ π‘Ž βˆ’ 3 6 1 2
  • B π‘Ž
  • C √ 2 π‘Ž
  • D √ π‘Ž βˆ’ 1 9 2
  • E π‘Ž βˆ’ 3 6 1 2

Q4:

Find the geometric mean of π‘₯ βˆ’ 𝑦 2 2 and π‘₯ βˆ’ 𝑦 π‘₯ + 𝑦 .

  • A | π‘₯ βˆ’ 𝑦 |
  • B | π‘₯ + 𝑦 |
  • C π‘₯ + 𝑦 2 2
  • D | | π‘₯ βˆ’ 𝑦 | | 2 2

Q5:

Find the geometric mean of ( π‘₯ + 𝑦 ) 2 and ( π‘₯ βˆ’ 𝑦 ) 2 .

  • A | π‘₯ βˆ’ 𝑦 | 2 2
  • B π‘₯ + 𝑦 2 2
  • C | π‘₯ + 𝑦 |
  • D | π‘₯ βˆ’ 𝑦 |

Q6:

Find the geometric mean of π‘₯ 3 and 9 π‘₯ 𝑦 3 1 6 .

  • A 3 | | π‘₯ | | 𝑦 3 8
  • B 9 | | π‘₯ | | 𝑦 3 8
  • C 9 | | 𝑦 | | π‘₯ 3 8
  • D 3 | | 𝑦 | | π‘₯ 3 8

Q7:

Find the geometric mean of the numbers 6 , 7 2 , 1 0 8 a n d .

Q8:

Find the geometric means of the sequence ( 2 , … , … , … , 4 8 0 2 ) .

  • A 1 4 , 9 8 , 6 8 6 or βˆ’ 1 4 , 9 8 , βˆ’ 6 8 6
  • B 1 6 , 1 2 8 , 1 0 2 4 or βˆ’ 1 6 , 1 2 8 , βˆ’ 1 0 2 4
  • C 1 6 , 1 2 8 , 1 0 2 4 , 8 1 9 2 or βˆ’ 1 6 , 1 2 8 , βˆ’ 1 0 2 4 , 8 1 9 2
  • D 1 4 , 9 8 , 6 8 6 , 4 8 0 2 or βˆ’ 1 4 , 9 8 , βˆ’ 6 8 6 , 4 8 0 2

Q9:

Find the geometric means of the sequence ( 4 , … , … , … , 1 0 2 4 ) .

  • A 1 6 , 6 4 , 2 5 6 or βˆ’ 1 6 , 6 4 , βˆ’ 2 5 6
  • B 2 0 , 1 0 0 , 5 0 0 or βˆ’ 2 0 , 1 0 0 , βˆ’ 5 0 0
  • C 2 0 , 1 0 0 , 5 0 0 , 2 5 0 0 or βˆ’ 2 0 , 1 0 0 , βˆ’ 5 0 0 , 2 5 0 0
  • D 1 6 , 6 4 , 2 5 6 , 1 0 2 4 or βˆ’ 1 6 , 6 4 , βˆ’ 2 5 6 , 1 0 2 4

Q10:

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
  • C100, 196
  • D196, 292
  • E4, 92

Q11:

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

  • A 4 8 , 2 7
  • B 1 8 , 2
  • C 3 9 , 1 8
  • D 2 7 , 6

Q12:

The three sides of a right triangle are in a geometric sequence with a common ratio π‘Ÿ < 1 . Find π‘Ÿ .

  • A ο„Ÿ √ 5 + 1 2
  • B βˆ’ ο„Ÿ √ 5 βˆ’ 1 2
  • Ccannot be determined
  • D βˆ’ ο„Ÿ √ 5 + 1 2
  • E √ 5 + 1 2

Q13:

Insert five positive geometric means between 2 1 3 8 and 6 7 2 1 9 .

  • A 2 1 1 9 , 4 2 1 9 , 8 4 1 9 , 1 6 8 1 9 , 3 3 6 1 9
  • B 2 1 7 6 , 2 1 1 5 2 , 2 1 3 0 4 , 2 1 6 0 8 , 2 1 1 2 1 6
  • C βˆ’ 2 1 7 6 , 2 1 1 5 2 , βˆ’ 2 1 3 0 4 , 2 1 6 0 8 , βˆ’ 2 1 1 2 1 6
  • D βˆ’ 2 1 1 9 , 4 2 1 9 , βˆ’ 8 4 1 9 , 1 6 8 1 9 , βˆ’ 3 3 6 1 9

Q14:

Insert three positive geometric means between 1 and 8 1 1 6 .

  • A 3 2 , 9 4 , 2 7 8
  • B 6 , 3 6 , 2 1 6
  • C 2 3 , 4 9 , 8 2 7
  • D βˆ’ 2 3 , 4 9 , βˆ’ 8 2 7
  • E βˆ’ 3 2 , 9 4 , βˆ’ 2 7 8

Q15:

Find the geometric mean of 16 and 4.

Q16:

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

  • A36, 49
  • B49, 134
  • C2, 21
  • D2, 83
  • E36, 121

Q17:

Insert four geometric means between 1 4 and 256.

  • A 1 , 4 , 1 6 , 6 4
  • B 1 2 , 1 , 2 , 4
  • C 1 , βˆ’ 4 , 1 6 , βˆ’ 6 4
  • D 1 , βˆ’ 1 4 , 1 1 6 , βˆ’ 1 6 4
  • E 1 , 1 4 , 1 1 6 , 1 6 4

Q18:

Insert two geometric means between 2 9 and 6.

  • A 2 3 , 2
  • B 1 3 , 1 2
  • C 2 3 , βˆ’ 2
  • D 3 2 , βˆ’ 1 2
  • E 3 2 , 1 2

Q19:

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.

Q20:

Find the number of geometric means inserted between 97 and 6 208 given the sum of the last two means equals eight times the sum of the first two means.

Q21:

Find the geometric mean of 3 2 and 6 2 .

Q22:

Find the geometric mean of 9 π‘₯ 3 6 and 3 6 𝑦 4 0 .

  • A 1 8 π‘₯ 𝑦 1 8 2 0
  • B 1 8 π‘₯ 𝑦 9 1 0
  • C 1 8 π‘₯ 𝑦 9 2 0
  • D 1 8 π‘₯ 𝑦 1 8 1 0

Q23:

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

Q24:

How many geometric means are inserted between 13 and 208 so that the product of the second mean and the last mean is βˆ’ 5 4 0 8 ?
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