Answer:
(a) Arithmetic? No. Geometric? YES!
(b) The terms will never become zero or negative.
Step-by-step explanation:
<h2>
Explaining part (a)</h2>
An aritmetic sequence has the same difference between each term, positive or negative.
Example: 1, 4, 7, 10, 13, ... the difference between consecutive terms is always 3
Example: 0, -2, -4, -6, -8, ... the difference between consecutive terms is always -2
A geometric sequence has the same ratio (or multiplier) between consective terms, positive or negative, causing an increase or a decrease.
Example: 1, 2, 4, 8, 16, ... each term is 2x the term before it
Example: 64, 32, 16, 8, 4, 2, 1, (1/2), (1/4), (1/8), ...each term is half the term before
Example: +91, -27, +9, -3, +1, -1/3, +1/9. -1/27, ... each term is -1/3 of term before
In the given sequence, we can see that the difference between terms is not always the same number. 100 - 50 = 50, but 50 - 25 = 25, not 50.
However, we do see that each term is half the term before it. That is definitely geometric.
<h2>
Explaining part (b)</h2>
For 100, 50, 25, 12.5, ... we get each term by multiplying the previous term by (1/2), which is a positive number. No matter how many times you multiply by a positive, you'll never get a negative or get a zero.
Multiply by 1/2 enough times, and you get as small a positive number as you like, but it will always be positive, even if you get down to billionths or trillionths.
