This week, we learned about arithmetic sequences and the different formulas to solve these sequences. In this blog post, I am going to show you the different formulas to simplify these arithmetic sequences.

Let’s say we have this sequence:

1, 4, 7, 10, 13…

First we need to find the difference in this pattern.

Look at the amount that this sequence jumps each time, we know that the difference is 3

To find the general rule, we use this formula:

Tn= + (n=1)(d)

Now all you need to do is plug in the information and do the algebra.

Tn=1+(n-1)(3)

Tn=1+3n-3

Tn=3n-2

Now, let’s say we wanted to find out what would be.

Then we add the first term to the difference 11 times.

= 1+(11)(3)

= 34