Question

The sum of 3 numbers in a geometric progression is 65, the product of these 3 numbers is 3375. Determine these 3 numbers.

Answer 1

The 3 numbers are 5, 15, 45.

Explanation:

Let the three numbers in G.P be $\frac{a}{r}$, a, ar.

Given: Sum of the G.P ($\frac{a}{r}$+ a + ar) = 65

Product of the G.P (a³) = 3375

a³ = 3375

a = $\sqrt[3]{3375}$

a = 15

Substituting the value of a, we get

$\frac{a}{r}$+ a + ar = 65

$a(\frac{1}{r} + 1 + r) = 65$

1 + r + r² = 65r ÷ 15

r² + r + 1 = 13r ÷ 3

r² + r = 10r ÷ 3

3r² - 10r + 3 = 0

(3r - 1) (r - 3) = 0

r = 3, $\frac{1}{3}$

When a = 15, r = 3 the three numbers of G.P is 5, 15, 45.

a = 15, r = $\frac{1}{3}$ the three numbers of G.P is 45, 15, 5.

To know more:

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