# How do you find the 93rd term of the arithmetic sequence with first term 23 and 10th term 77?

Jul 1, 2017

$575$

#### Explanation:

The formula for an arithmetic sequence is $a + \left(n - 1\right) d = x$

Here you already have the first term, $a = 23$.

Now you just have $23 + \left(10 - 1\right) d = 77 \equiv 9 d = 54 \equiv d = \frac{54}{9} = 6$.

Now you have $a$ and $d$. For the 93rd term, we do $23 + \left(93 - 1\right) 6 = 23 + \left(92\right) 6 = 575$.