Question

How do I find the formula for the nth term in a sequence? Like for example the sequence:4,9,14,19 what is the next term?

Answer 1

Explanation:

Arithmetic sequence:

a = first term = 4

d = common difference = second term - first term

= 9 - 4

d = 5

`\sf t_n =a +(n -1)*d`

= 4 + (n - 1) *5

= 4 + 5n - 5

= 5n -1

Check; n= 1 , first term = 5*1 - 1 = 5 - 1 = 4

n = 2, second term = 5*2 - 1 = 10 -1 = 9

n = 3, third term = 5*3 - 1 = 15 - 1 = 1

The next term, fifth term = 5*5 - 1

= 25 - 1

= 24