# What is the 110th term of -1, -4, -7?

##### 1 Answer

$- 328$

#### Explanation:

Think of the sequence of 1, 4, and 7 first. This might help a bit.

Let's say that each term is $n$. For 4 (the second term), $n = 2$ and for 7 (the third term), $n = 3$.

There are many formulas you can get, but the easiest for me is $3 n - 2$.

Here, $n = 110$, so $3 \cdot 110 - 2 = 330 - 2 = 328$. However, the sequence is negative so the answer would be $- 328$.

Another way to do this would be to do $3 \cdot \left(n - 1\right) + 1$. This works because, using $n = 2$, $3 \cdot \left(2 - 1\right) + 1 = 4$. This works for every single term. $3 \cdot \left(110 - 1\right) + 1 = 3 \cdot 109 + 1 = 327 + 1 = 328$.

Still another way to do this would be, instead of using positive numbers, to use either of the formulas $- 3 n + 2$ or $- 3 \cdot \left(n - 1\right) - 1$. These formulas would save you from having to turn the sign at the last step and would also prevent silly errors.