datermine the Three geometric means between 2 and 81/8​

Sagot :

Answer:

The geometric means between 2 and 81/8 are 3, 9/2, 27/4.

Thus, the sequence becomes 2, 3, 9/2, 27/4, 81/8.

Step-by-step explanation:

Find the common ratio using the formula an=a1•r^n-1

an=a1•r^n-1

a5=a1•r^4

81/8=2r^4

(Divide both sides by 2)

81/16=r^4

Take the root of both sides and use positive and negative roots.

(See the solution on how to get the root in the picture)

Therefore the common ratio or r is 3/2.

Solve now for a2, a3, a4.

an=a1•r^n-1

a2= 2(3/2)^1

a2=3

an=a1•r^n-1

a3=2(3/2)^2

a3=2(9/4)

a3=18/4

a3=9/2

an=a1•r^n-1

a4=2(3/2)^3

a4=2(27/8)

a4=54/8

a4=27/4

View image KENTHARVZ42