# How do you find the 9th term of the arithmetic sequence a10 = 100 and a20 = 50?

##### 1 Answer

#### Explanation:

Given: arithmetic sequence:

An arithmetic sequence has the form:

**Find #d#:**

We have two equations and two unknowns. Use elimination.

Multiply the second equation by

Equation 1:

Equation 2 *(-1) =

**Find #a_1#** by substitution:

Simplify:

**CHECK: values of # a_1# and #d#**

#a_10 = 145 + 9*(-5) = 100

#a_20 = 145 + 19*(-5) = 50

**Find #a_9#:**

**Does this answer make sense?**

Yes, because