# How do you find the 15th term in the arithmetic sequence -3, 4, 11, 18...?

Oct 21, 2016

$95$

#### Explanation:

To find the ${n}^{t h}$ term, we use the formula $\textcolor{red}{{x}_{n} = a + d \left(n - 1\right)}$, where $n$ is the term you are looking for, $a$ is the ${1}^{s t}$ term and $d$ is the difference between terms (it does not vary)

From the arithmetic sequence $- 3 , 4 , 11 , 18. . .$, we can see that $a = - 3$ and $d = 7$

You can find $d$ by subtracting a number by its precedent $\implies d = 4 - \left(- 3\right) = 7$ or $d = 11 - 4 = 7$ and so on! It's always going to be the same value.

So, ${x}_{15} = - 3 + 7 \left(15 - 1\right) = - 3 + 7 \left(14\right) = - 3 + 98 = 95$

Another way to do this since it's "only" the ${15}^{t h}$ term is by hands or calculator. They already gave you the four terms, which will help you find the difference "$d$". Use only the first term "$- 3$" and add 7 until you reach the ${15}^{t h}$ term.

$\implies - 3 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 95$

Hope this helps :)