# How do you write a rule for the nth term of the arithmetic sequence and then find a_10 for -4, 2, 8, 14, 20?

Feb 25, 2017

Tenth term ${a}_{10}$ in given sequence is $50$.

#### Explanation:

In an arithmetic sequence, the difference between acreen and its immediately preceding term is always constant. This is called as 'common difference'.

Let us check here. Here, we have $2 - \left(- 4\right) = 8 - 2 = 14 - 8 = 20 - 14 = 6$.

Hence, here we have an arithmetic sequence with first term ${a}_{1} = - 4$ and common difference $d$ equal to $6$.

In an arithmetic sequence if first term is ${a}_{1}$ and common difference is $d$, then $n \left(t h\right)$ term ${a}_{n}$ is given by ${a}_{n} = {a}_{1} + \left(n - 1\right) d$.

Hence, tenth term in given sequence is

-4+(10-1)×6=-4+9×6=-4+54=50.