Number Sequencing Help plz??

Question

Find Tn for each arithmetic sequence:
5, -1, -7, ...
Answer is 11-6n ( for all the morons who keep telling me to just subtract six) please show me how to get there

Answer 1

Hi again. I will repeat my answer here as from the other question:
(not a moron lol)


Notice how for each sequential value, you are reducing it by 6. The formula for your sequence is:

11-6n

Where n here refers to 1st, 2nd, 3rd etc numbers. Just plug in the "n" depending on which number you want. For example, in your sequence, I want to find out the 110th number. If you had to do it by hand it would take forever. But using my formula it is easy as cake:

11-6*110=-93

How did I come up with that nifty formula. Well, I knew the first value had to be 5, and I also knew I was subtracting 6. From what value can I take away 6 and get 5? 11, right? I also knew that as you went along in the sequence, you were taking away -6 each time you repeated the pattern n times, or -6*n. Thus I get

11-6n

It is actually pretty fun to try yourself on a different sequence. Say I give you:

1,5,9,13...

What's the formula?

This one is a bit more tricky, but not too hard. First, I know I add 4 each time. One formula might be:

-3 + 4n

so the 1st will be:

-3+4(1)=1
2nd will be:
-3+4(2)=5
-3+4(3)=9

But we can also have other formulas.

1+4(n-1)
So:
1st: 1+4(1-1)=1
2nd: 1+4(2-1)=5
3rd: 1+4(3-1)=9
4th: 1+4(4-1)=13