# The third term of an arithmetic sequence is 9 and the seventh term is 31, how do you find the sum of the first twenty-two terms?

##### 1 Answer

The sum of the first 22 terms is

#### Explanation:

We know that

We also know that

**Equation (1): **

and

**Equation (2): **

Subtract Equation (2) from Equation (1).

**Equation (3): **

Substitute Equation (3) in Equation (1).

So

So the 22nd term is given by

The sum

So