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.
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:
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