Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 3, comma, 12, comma, 48, comma, point, point, . 3,12,48,...
To determine whether the sequence 3, 12, 48,... is arithmetic or geometric, we can check if there is a constant common difference between consecutive terms.
To check if it is arithmetic, we can see if there is a constant difference between terms. The difference between the second term (12) and the first term (3) is 12 - 3 = 9. The difference between the third term (48) and the second term (12) is 48 - 12 = 36. Since the differences are not the same, the sequence is not arithmetic.
Next, we can check if it is geometric by dividing each term by the previous term.
The ratio between the second term (12) and the first term (3) is 12 / 3 = 4. The ratio between the third term (48) and the second term (12) is 48 / 12 = 4.
Since the ratios are the same, the sequence is geometric. The common ratio is 4.