Answer: A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.
This ratio is known as a common ratio.
Given is the function as -
f(x) = (1) ∙ (1/4)ˣ - 1
Now -
for {x} = 1, we can write -
f(1) = (1) ∙ (1/4) - 1 = 1/4 - 1 = -3/4 = a{1}
for {x} = 2, we can write -
f(2) = (1) ∙ (1/16) - 1 = 1/16 - 1 = -15/4 = a{2}
for {x} = 3, we can write -
f(2) = (1) ∙ (1/64) - 1 = 1/64 - 1 = -63/4 = a{3}
So, we can write -
a{2}/a{1} = a{3}/a{2}
(- 15/4)/(- 3/4) = (- 63/4)/(- 15/4)
15/4 x 4/3 = 63/4 x 4/15
5 ≠ 63/15
Therefore, the function f(x) = (1) ∙ (1/4)ˣ - 1, does not represent a geometric sequence.
Explanation: