# What is the general term of an arithmetic sequence with t_1 = 5 and t_2 = 2?

Apr 13, 2017

$C$

#### Explanation:

The general term of an arithmetic sequence is given by

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

We're given that the first term is $5$ and the second term is $2$. This means that $d = - 3$, so:

$a \left(n\right) = 5 - 3 \left(n - 1\right)$

We note that $n < 1$, because if the sequence starts at ${t}_{1}$. Therefore, the domain is n ≥ 1.

If we check, we realize that

$a \left(1\right) = 5 - 3 \left(1 - 1\right) = 5 = {t}_{1}$

Which is what we wanted to obtain.