Finding the middle one

Algebra Level 1

Three possitive numbers a , b and c are first three terms of a GP If it is known that:- $a \times b \times c = 27$ Find out the value of b

The answer is 3.

3 solutions

Rick B
Aug 21, 2014

Let's say that $b = ar$ and $c = ar^2$ . The product will become $a \times ar \times ar^2 = a^3r^3 = (ar)^3 = b^3 = 27 \implies b = \sqrt [3] {27} = \boxed{3}$

LET [A] BE a/r [B] be a AND[ C ] BE ar THEREFORE a/rXaXar=3

Achal Goyal - 6 years, 8 months ago

David Patty
Aug 21, 2014

Consider all possible factors of 27; that is, 1, 3, 9. If abc = 27 they must each contain one of these three numbers, and since abc is a GP the numbers must increase with each term. Therefore, a = 1, b = 3, c = 9, with the common ratio obviously being 3.

What is GP

Aareyan Manzoor - 6 years, 8 months ago

A GP is a special type of series in which each preceding element is multiplied by a common factor or ratio for eg : 1,3,9,27....... is a gp with common ratio 3 To find the common ratio divide the second number by the first number of the series.

Athiyaman Nallathambi - 5 years, 11 months ago

Same thinking here

Sem David Sitanggang - 6 years, 9 months ago

While it still yields a b-value of 3, the GP could be 1/3, 3, 27.

James Moors - 6 years, 8 months ago

Sophie Crane
Sep 27, 2014

$a,b,c=1,3,9$

Finding the middle one

The answer is 3.

3 solutions

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