Final answer:
To find the nth term of the geometric sequence (one half, 8, 128, 2048, ...), we use the formula an = a1 × rn-1 with the first term a1 being one half and the common ratio r being 16. The nth term equation is thus an = (1/2) × 16n-1.
Step-by-step explanation:
The sequence given is a geometric sequence where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. In this case, the common ratio is 16 because 8 is 16 times one half, 128 is 16 times 8, and so on. The formula for the nth term of a geometric sequence is an = a1 × rn-1, where a1 is the first term and r is the common ratio.
an for our sequence can be calculated by plugging in the given first term (1/2) and the common ratio (16), resulting in the nth term formula: an = (1/2) × 16n-1. This represents exponential growth, with each term increasing by a factor of 16 compared to the previous term.