# How do you write a rule for the nth term of the arithmetic sequence given a_5=10, a_12=24?

Aug 29, 2016

${n}^{t h}$ term ${a}_{n} = 2 n$

#### Explanation:

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

Here, we have ${a}_{5} = {a}_{1} + 4 d = 10$ and ${a}_{12} = {a}_{1} + 11 d = 24$. Subtracting former from latter equation, we get

$7 d = 14$ or $d = \frac{14}{7} = 2$ and a_1=10-4d=10-4×2=10-8=2.

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

= 2+(n-1)×2=2+2n-2=2n