What is the difference between arithmetic and geometric sequences

In arithmetic sequences the numbers are related by a sum of a constant number while in geometric sequences the numbers are related by a product of a constant number.

Step-by-step explanation:

In arithmetic sequences the numbers are related to the prior by the sum of a constant number 'r'. So if the first number of a sequence is 1 and the ratio of this sequence is 3, the next number will be 1 + 3 = 4, while the next after that will be 4 + 3 = 7 and so on. Forming a sequence of {1,4,7,10,13,16, ... }. While in geometric sequences the numbers are related by a product of a costant number 'q', in these cases to find the next number we need to multiply the prior by the constant 'q', so if the first number of this sequence is 1 and the ratio is 3, the next number will be 1*3 = 3, while the next after that will be 3*3 = 9 and so on forming a sequence of {1,3,9,27,81, ... }.