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 #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.