# The first two terms of an arithmetic sequence are a_1 = 2 and a_2 = 4. What is a_10, the tenth term?

Mar 17, 2018

color(indigo)(a_10 = 20

#### Explanation:

${a}_{1} = 2 , {a}_{2} = 4$

Common Difference $d = {a}_{2} - {a}_{1} = 4 - 2 = 2$

nth term of an Arithmetic Sequence is given by the formula,

${a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$

Given ${a}_{1} = 2 , n = 10$ and we found $d = 2$

:. color(indigo)(a_10) = 2 + (10-1)*2 = 2 + 18 color(indigo)(= 20