If Three Geometric Means Are Inserted Between 1 And 256,Find The Third Geometric Mean.( Need A Solution)

If three geometric means are inserted between 1 and 256,find the third geometric mean.( need a solution)

 

Answer:

1, 4, 16, 64, 256.

a3 = 16

Step-by-step explanation:

We will use the geometric sequence formula which is: an = a1 x r^(n - 1)

First write all the given which are:

  • a1 = 1 (The first term)
  • an = 256 (The last term)
  • n = 5 (number of terms)

Now, lets substitute all the given.

  • an = a1 * r^(n - 1)
  • 256 = 1 * r^(5 - 1)

Simplify first the exponent.

  • 256 = 1 * r^4

You will not add the 1 to 256, because 1 is like the coefficient of r^4

So what will you do is divide both sides by 1.

  • 256 = r^4

Now get the root or both sides.

  • 4 = r

Now, lets check if it is correct. Multiply the next term with 4

  • a1 = 1
  • a2 = 4
  • a3 = 16
  • a4 = 64
  • a5 = 256

An yore finding the third mean of the geometric sequence. The third mean is a3 = 16


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