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guajiro [1.7K]
3 years ago
13

A geometric sequence has an initial value of 1/2 and a common ratio of 8. Write an exponential function to represent this sequen

ce.
A: f(X) = 8· (1/2)^x
B: f(X) = 8· (1/2)^-1
C: f(x) = 1/2 ·8^x
D: f(x) = 1/2 ·8^x-1

please help me
Mathematics
2 answers:
Airida [17]3 years ago
8 0

Answer:

The correct option is  D.

Step-by-step explanation:

It is given that the initial value of a GP is 1/2 and common ratio is 8. It means

a_1=\frac{1}{2}

r=8

The nth term of a GP is

a_n=a_1r^{n-1}

where, a_1 is inital value and r is common ratio.

Substitute a_1=\frac{1}{2} and r=8 in the above formula.

a_n=\frac{1}{2}(8)^{n-1}

The exponential function to represent this sequence is

f(x)=\frac{1}{2}(8)^{x-1}

Therefore the correct option is D.

marusya05 [52]3 years ago
6 0

Answer:

D

Step-by-step explanation:

the n th term of a geometric sequence is

a_{n} = ar^{n-1}

Where a is the first term and r the common ratio

here a = \frac{1}{2} and r = 8, hence

f(x) = \frac{1}{2}(8)^{x-1} → D


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