Determine whether each sequence is arithmetic or geometric. 2, 14, 98, 686, . . -5, -10, -15, -20, . . a. both sequences are geometric. b. the first sequence is geometric. the second sequence is arithmetic. c. both sequences are arithmetic.

Choice B) First is geometric. Second is arithmetic.



For the sequence {2, 14, 98, 686, ...} we start off with 2 and multiply that by 7 to get the next term (14) and then multiply that by 7 to get the term after that (98) and so on. The common ratio is 7. We can see this by dividing any term by its previous one. For example, 98/14 = 7.

The sequence {-5, -10, -15, -20, ...} is arithmetic because we subtract 5 each time to generate the next term. This is the same as adding -5 each time. Therefore the common difference is -5. To find the common difference, pick any term you want and subtract off the previous term. Example: -15 - (-10) = -15+10 = -5.