Question

What is the explicit formula for this geometric sequence? 8, 4 2, 1

a) a_(n)=(1)/(2)*8^((n-1))
b) a_(n)=2*8^((n-1))
c) a_(n)=8*((1)/(2))^((n-1))
d) a_(n)=8*2^((n-1))

Answer 1

C

Explanation:

Recall that the standard form for the explicit formula of a geometric sequence is given by:

`a_n=a\cdot(r)^(n-1)`

Where a is the initial term, r is the common ratio, and n is the nth term.

Our sequence is 8, 4, 2, 1, and so on.

Hence, our initial term a is 8.

Each subsequent term is half of the previous one. So, our common ratio r is 1/2.

Therefore, by substitution, we acquire:

`\displaystyle a_n=8\cdot\left((1)/(2)\right)^(n-1)`

In conclusion, our answer is C.