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

Q1:

Find π¦ given the geometric mean between 2 and π¦ is 10.

Q2:

The ratio π₯ βΆ 4 = 4 βΆ π¦ , so 4 is the geometric mean of π₯ and π¦ . Find the geometric mean of ο½ π₯ + 1 π¦ ο and οΌ π¦ + 1 π₯ ο .

Q3:

Find the geometric mean of ( π β 1 9 ) and ( π + 1 9 ) .

Q4:

Find the geometric mean of π₯ β π¦ 2 2 and π₯ β π¦ π₯ + π¦ .

Q5:

Find the geometric mean of ( π₯ + π¦ ) 2 and ( π₯ β π¦ ) 2 .

Q6:

Find the geometric mean of π₯ 3 and 9 π₯ π¦ 3 1 6 .

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 , β¦ , β¦ , β¦ , 4 8 0 2 ) .

Q9:

Find the geometric means of the sequence ( 4 , β¦ , β¦ , β¦ , 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.

Q11:

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

Q12:

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

Q13:

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

Q14:

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

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.

Q17:

Insert four geometric means between 1 4 and 256.

Q18:

Insert two geometric means between 2 9 and 6.

Q19:

Find the number of geometric means inserted between 82 and 1β312 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 6β208 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 π¦ 4 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 β 5 4 0 8 ?

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