If Three Geometric Means Are Inserted Between 1 And 256, Find The Third Geometric Mean., A. 64 , B. 32 , C. 16 , D. 4

If three geometric means are inserted between 1 and 256, find the third geometric mean. a. 64
b. 32
c. 16
d. 4

 

Geometric Sequence

Finding the Geometric Means

The third geometric mean between 1 and 256 is 64.

Solution:

Geometric Sequence Formula: x_n = arⁿ⁻¹ where;

  • a - first term
  • r - common ratio
  • n - number of terms in the sequence.

Thus, a = 1, r = ?, n = 5

x₅ = ar⁵ ⁻ ¹

256 = 1r⁵ ⁻ ¹

256/1  = r⁴

/1

256 = r⁴

⁴√256 = ⁴√r⁴

4 = r

Using r = 4, find the second term. Thus, X₂  = (1)(4)²⁻¹

X₂  = 4¹

X₂ = 4

Find for the third term. Thus, X₃ = (1)(4)³⁻¹

X₃ = 4²

X₃ = 16

Find for the fourth term. Thus, X₄ = (1)(4)⁴⁻¹

X₄ = 4³

X₄ = 64

Therefore, the geometric sequence will be 1, 4, 16, 64, 256 where the third geometric mean is 64.

Code: 10.3.1.1

For more details regarding geometric means and sequence, go to the following links:

brainly.ph/question/187815

brainly.ph/question/304404

brainly.ph/question/841122


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