Question

Insert 5 geometric means between 7/4 and 112.​

Answer 1

Answer:

7/2, 7, 14, 28, 56

Step-by-step explanation:

a = 7/4 -----------------> eq 1

a/r⁶ = 112 --------------> eq 2

eq 1 ÷ eq 2

ar⁶/a = 7/4 ÷ 112

r⁶ = 1/4 ÷ 16

r⁶ = 1/2⁶

r = 1/2

so the numbers are

= a/r, a/r², a/r³, a/r⁴, a/r⁵

= 7/2, 7, 14, 28, 56

Answer 2

Given : 7/4  and 112​

To Find : Insert 5 geometric means

Solution:

Let say a  = 7/4

r is the common ration

7/4  , ar , ar² , ar³  , ar⁴  , ar⁵   , 112

ar , ar² , ar³  , ar⁴  , ar⁵ are 5   geometric means

112  =(7/4)r⁶

=> r⁶ = 64

=> r = ± 2

5  geometric means can be

7/2 , 7 , 14 , 28 , 56

or

-7/2 , 7  , - 14 , 28 , - 56

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