Question

Write the geometric sequence in function notation.

4, 2, 1, 1/2 ,1/4,...
A) f(x) = (2) · (1/4)x-1
B) f(x) = (2) · (1/2)x-1
C) f(x) = (4) · (1/4)x-1
D) f(x) = (4) · (1/2)x-1

Answer 1

The correct function notation for the geometric sequence is D) f(x) = (4) · (1/2)x-1, since the first term is 4 and the common ratio is 1/2.

Step-by-step explanation:

To write the geometric sequence 4, 2, 1, 1/2 ,1/4,...

in function notation, we need to identify the first term and the common ratio of the sequence. The first term (a

1

) is 4, and the common ratio (r) can be found by dividing any term by its preceding term, which is

1/2

in this case. So, the nth term of the sequence can be found using the formula a

n

= a

1

· r

(n-1)

.

Applying this formula, the function notation for our sequence is:

f(x) = a1 · r(x-1)

f(x) = 4 · (1/2)(x-1)

Therefore, the correct option using function notation for the given geometric sequence is:

D) f(x) = (4) · (1/2)x-1