# How do you find a_100 when a_1=-30, d=5?

Aug 1, 2017

${a}_{100} = 465$

#### Explanation:

Since this problem uses $d$, the common difference, we know this is an arithmetic sequence.

The general formula for an arithmetic sequence is ${a}_{n} = {a}_{1} + \left(n - 1\right) d$, where ${a}_{n}$ is the ${n}^{t h}$ term, ${a}_{1}$ is the first term, and $d$ is the common difference.

Since we already know that ${a}_{1} = - 30$ and $d = 5$, we can substitute these values into the formula.

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

${a}_{n} = - 30 + \left(n - 1\right) 5$

To find ${a}_{100}$, substitute $100$ for $n$.

${a}_{100} = - 30 + \left(100 - 1\right) 5$

Now, we can simplify.

${a}_{100} = - 30 + \left(99\right) \left(5\right)$

${a}_{100} = - 30 + 495$

${a}_{100} = 465$