Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

The GM of a series of a three positive numbers is 4 by including fourth number it becomes 2 what is fourth value

Sagot :

oladayoademosu

Answer:

1/4

Step-by-step explanation:

Let a₁, a₂, a₃ and a₄ be the four numbers. Since the geometric mean of the first 3 positive numbers is 4, we have that

∛(a₁a₂a₃) = 4. (1)

Also the geometric mean of the four numbers is 2, we have that ⁴√(a₁a₂a₃a₄) = 2   (2).

So, taking the cube of (1), we have

[∛(a₁a₂a₃)]³ = 4³

a₁a₂a₃ = 64  (3)

Also, taking the fourth power of equation (2), we have

[⁴√(a₁a₂a₃a₄)]⁴ = 2⁴  

a₁a₂a₃a₄ = 16  (4)

Dividing (4) by (3), we have

a₁a₂a₃a₄/a₁a₂a₃ = 16/64

a₄ = 1/4

The fourth value is 1/4

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.