Question

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

Answer 1

`-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 `3n-2`.

Here, `n=110`, so `3*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*(n-1)+1`. This works because, using `n=2`, `3*(2-1)+1=4`. This works for every single term. `3*(110-1)+1=3*109+1=327+1=328`.

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