How Do We Find A Formula For A Simple Sequence?

Here is a question:

Find the 32nd term of the sequence

6, 11, 16, 21....

1. Find the difference between the numbers

So 11-6 or 21-16 will give 5

2. 5 is the difference so we have the first part of our nth term equation.

3. The nth term will be similar to an+b

4 We have to find a and b.

5. The difference between the number will give you a. We found a from the above sequence and it was 5

6. So a=5 which means we have 5n + b, we need to find b

7. In the sequence above we have

6, 11, 16, 21... the difference is 5=a

b is the zero term. In the above 6 is the first term and 11 the second and 16 the third and so on.

So the zero term is the number before 6

We are adding 5 each time so to find the zero term we must go back so we subtract 5 from 6 and get...1 and its +1.

So now we look at the nth term an + b

a=5 and b=+1 sun into the formula

5n+1. Now to find the 34th term, where n=34 so sub into the formula found.

5n+1= 5x34+1

= 170+1

= 171

So the 34th term is 171.