Question

If the sum of three numbers in G.P is 38, and their product is 1728, find the numbers.

Answer 1

The numbers are 8,12 and 18. The ratio of 12 and 8 is 3/2. And the ratio of 18 and 12 is also 3/2 by this we can prove that the numbers 8,12 and 18 are in G.P.and the product of 8,12,18 is 1728. By this we get the answer as 8,12,18.

Answer 2

AnswEr:

Let the terms of the G.P be $\sf{a}{r}$ , a, ar. It is given that

$\qquad \tt \: \frac{a}{r} + a + ar = \frac{39}{10} \: \: \: \: and \\ \\ \qquad \tt \frac{a}{r} \times a \times ar = 1$

$\rightarrow \tt \: a( \frac{ {r}^{2} + r + 1 }{r} ) = \frac{39}{10} \: \: \: and \: \: \: {a}^{ 3} = 1 \\ \\ \rightarrow \tt \: 10( {r}^{2} + r + 1) = 39r \\ \\ \rightarrow \tt \: 10 {r}^{2} - 29r + 10 = 0 \\ \\ \rightarrow \tt \: (2r - 5)(5r - 2) = 0 \\ \\ \tt \rightarrow \: r = \frac{5}{2} \: \: \: or \: \: \: r = \frac{2}{5}$

• Hence, the numbers are 2/5, 1, 5/2 or 5/2, 1, 2/5.

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Geometric Progressions -

A sequence of non-zero numbers is called geometric Progressions. If the ratio of a term and the term preceding to it always a constant quantity.

The constant ratio is called the common ratio of the G.P.