How do you solve arithmetic sequences

Question

How do you find the next numbers in a sequence 

Answer 1

Explicit definition:

a_n = a₁ + (n - 1)d

Recursive definition

a_{n + 1} = a_n + d

 

BTW, equations have solutions. A sequence is a list of numbers.

Answer 2

You have to come up with a way to represent the next number given the previous numbers.

 

For example, suppose your sequence is 1, 2, 3, 4, 5, x

 

You know that  n1 = 1, n2 = 2, n3 = 3

 

Therefore, you can represent the value of the next number f(n+1) in terms of the value of the previous number f(n) as follows:

 

f(n+1) = f(n) + 1

 

Therefore, f(6) = f(5) + 1.

Since we know that f(5) = 5, then f(6) = 5 + 1 = 6.