Determine whether the given sequence could be geometric, arithmetic, or neither. if possible, identify either the common ratio or the common difference. 4, 2, 1, 1/2

ARITHMETIC CHECK: A sequence is said to be arithmetic if any two consecutive terms differ by the same constant.

So, the test to check if a series is arithmetic is to compute consecutive differences, and see if they all return the same number.

If we subtract the first two terms, we have . If we subtract the third and second terms, we have .

These two differences returned two different values, so the series is not arithmetic.

GEOMETRIC CHECK: A sequence is said to be geometric if any two consecutive terms are in the same ratio.

So, the test to check if a series is geometric is to compute consecutive ratios, and see if they all return the same number.

If we divide the first two terms, we have

If we divide the third and second terms, we have

Finally, if we divide the last two terms we have

So, all ratios return the same number. This means that the series is geometric, and the common ratio is 1/2

answer: r there any options?

step-by-step explanation: