Question

Which graph represents a geometric sequence?

Answer 1

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: