5n, -n, 7n...
2a-5, 2a+2, 2a+9...
I'm having trouble with the variables. Any problem solving help?
For the simplest n'th term sequence, the formula is $\displaystyle \mathrm{n^{\mathrm{th}} \ Term} = dn+(a-d)$ where $\displaystyle d$ is the difference between the terms, $\displaystyle a$ is the first initial term and $\displaystyle n$ is the term number. Thus for $\displaystyle 3,4.5, 6$, the difference between the term ($\displaystyle d$) is $\displaystyle +1.5$, the first term ($\displaystyle a$) is $\displaystyle 3$ thus the formula is $\displaystyle \mathrm{n^{\mathrm{th}} \ Term} = (1.5)n + (3-1.5) = 1.5n + 1.5$.
For the second, do you mean $\displaystyle 5n, -n, -7n$? This would make the difference $\displaystyle -6n$, the first initial term $\displaystyle 5n$ and thus you would be able to use the n'th term formula.
Hi puzzled,
Are you sure about the first 3 terms of your first sequence? It would be nice if it were:
5n, -n, -7n
Then the common difference would be -6n. You simply add -6n four more times to get your four terms.
In the second one, 2a-5, 2a+2, 2a+9, you have a common difference of 7. Looks like each successive term is 7 more than the previous one. So, just add 7 four more times to get the next four terms.