Which represents the type of sequence: 12, 22, 30, 36, 41, …?
neither arithmetic nor geometric
both arithmetic and geometric
arithmetic
geometric
neither
The given sequence 12, 22, 30, 36, 41, … does not represent either an arithmetic or a geometric sequence. Therefore, the correct answer is "neither arithmetic nor geometric."
To determine the type of sequence, let's examine the given numbers: 12, 22, 30, 36, 41, ...
First, we can check if the sequence is arithmetic, meaning that the difference between consecutive terms is constant.
The differences between consecutive terms are: 10, 8, 6, 5, ...
Since the differences are not constant, we can conclude that the sequence is not purely arithmetic.
Next, we can check if the sequence is geometric, meaning that there is a common ratio between consecutive terms.
To find the ratio, we divide each term by the preceding term: 22/12 = 1.83, 30/22 = 1.36, 36/30 = 1.20, 41/36 = 1.14, ...
Since the ratios are not constant, we can conclude that the sequence is not purely geometric.
Therefore, the correct answer is "neither arithmetic nor geometric."