Question

Find an explicit formula for the geometric sequence 120, 60, 30, 15, ... . Note: The first term should be a(1).

a) a(n)=120⋅ 1/2^n-1

b) a(n)=120⋅(1/2)6n

c) a(n)=120⋅2^n

d) a(n)=120⋅ 1/2^n

Answer 1

The explicit formula for the given geometric sequence 120, 60, 30, 15, ... is a(n) = 120 * 1/2^(n-1).

Step-by-step explanation:

The given geometric sequence is 120, 60, 30, 15, ...

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant value called the common ratio. In this case, the common ratio is 1/2, since each term is half of the previous term.

We can find an explicit formula for this sequence using the formula a(n) = a(1) * r^(n-1), where a(n) is the nth term of the sequence, a(1) is the first term, r is the common ratio, and n is the term number.

Plugging in the values, we get a(n) = 120 * (1/2)^(n-1). Therefore, the correct option is a) a(n) = 120 * 1/2^(n-1).