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

Answer:

Step-by-step 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