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Trava [24]
3 years ago
15

Determine whether the given sequence could be geometric, arithmetic, or neither. if possible, identify either the common ratio o

r the common difference. 4, 2, 1, 1/2
Mathematics
1 answer:
REY [17]3 years ago
7 0

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 2-4 = -2. If we subtract the third and second terms, we have 1-2 = -1.

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

\dfrac{2}{4} = \dfrac{1}{2}

If we divide the third and second terms, we have

\dfrac{1}{2} = \dfrac{1}{2}

Finally, if we divide the last two terms we have

\dfrac{\frac{1}{2}}{1} = \dfrac{1}{2}

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



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