Question

Determine whether the sequence is an arithmetic​ sequence, a geometric​ sequence, or neither. If it is either arithmetic or​ geometric, give the next term in the sequence. 4096, 1024, 256, 64, 16,...

Answer 1

Answer: geometric series

Explanation:

If it is arithmetic, the difference from each term to the next will always be the same.

4096 - 1024 = 3072; 1024 - 256 = 768

3072 ≠ 768. so not arithmetic

If it is geometric, the ratio of each term to the next will always be the same.

4096/1024 = 4

1024/256 = 4

256/64 = 4

64/16 = 4

This is a geometric series. Each term (after the first) is (1/4) of the term before.

Hope this helps.