# How do you complete the statement for the arithmetic sequence: -14 is the __ term of 2 1/5, 2, 1 4/5,...?

Feb 20, 2017

82nd

#### Explanation:

We know that the nth term of an arithmetic sequence is given by ${t}_{n} = a + \left(n - 1\right) d$. Our first term is $2 \frac{1}{5} = \frac{11}{5}$ and our common difference is $- \frac{1}{5}$.

$- 14 = \frac{11}{5} + \left(n - 1\right) - \frac{1}{5}$

$- 14 = \frac{11}{5} - \frac{1}{5} n + \frac{1}{5}$

$- 14 = \frac{12}{5} - \frac{1}{5} n$

$- 14 - \frac{12}{5} = - \frac{1}{5} n$

$- \frac{82}{5} = - \frac{1}{5} n$

$n = \frac{- \frac{82}{5}}{- \frac{1}{5}}$

$n = 82$

Hopefully this helps!