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# Insert two geometric means between 32 and 62

### Question

Insert two geometric means between 32 and 62

### Options

A) (16, 32)

B) (40, 50)

C) (44.72, 52.87)

D) (47.25, 54.88)

### Explanation:

$$U_1 = a = 32$$
$$U_4 = ar^3 = 621$$
Assuming $$x$$ and $$y$$ are the geometric means
$$\cfrac{U_4}{U_1} =\cfrac{ar^3}{a} = \cfrac{125}{2 \times 32} = \cfrac{125}{64}$$
$$r^3 = \cfrac{125}{64}$$
$$r = \sqrt[3]{\cfrac{125}{64}} = \cfrac{5}{4}$$
$$x = U_2 = ar = 32(\cfrac{5}{4}) = 40$$
$$y = U_3 = ar^2 = U_2 \times r = 40 \times \cfrac{5}{4} = 50$$
The geometric means are (40, 50)

## Discussion (2)

• $$U_1 = a = 32$$
$$U_4 = ar^3 = 621$$
Assuming $$x$$ and $$y$$ are the geometric means
$$\cfrac{U_4}{U_1} =\cfrac{ar^3}{a} = \cfrac{125}{2 \times 32} = \cfrac{125}{64}$$
$$r^3 = \cfrac{125}{64}$$
$$r = \sqrt[3]{\cfrac{125}{64}} = \cfrac{5}{4}$$
$$x = U_2 = ar = 32(\cfrac{5}{4}) = 40$$
$$y = U_3 = ar^2 = U_2 \times r = 40 \times \cfrac{5}{4} = 50$$
The geometric means are (40, 50)