
Rate of increase
If I have two sequences A&B with starting points at t=0 of 5 and 8 respectively, then sequence A increases by 3 and sequence B by 2. i.ie
A: 5,8,11,14,17
B: 8,10,12,14,16
Ok so I know that at some stage sequence A will 'overtake' sequence B (as its increasing at a faster rate) at some stage (t=4 in the example ive thought up) but without writing out every number how can I just see or tell that at t=4 sequence A will 'overtake' sequence B.
Lcm? percentages? Im after the method?(Headbang)

Re: Rate of increase
You can do it by setting up an equation for the nth term of a sequence.
The "general term", $\displaystyle t$ of a sequence will be compared to the placement of the numbers in the sequence, $\displaystyle n$.
As sequence $\displaystyle 1$ increases at a rate of $\displaystyle 3$, $\displaystyle t=3n+k$, where $\displaystyle k$ is an unknown integer that we still need to work out. When $\displaystyle n=1$, $\displaystyle t=5$. Substituting this into the equation gives $\displaystyle 5=3+k$, so $\displaystyle k=2$ and the equation I was looking for is $\displaystyle t=3n+2$. You can check this by substituting in the other numbers of the sequence. Ie, when $\displaystyle n$ is $\displaystyle 2$, does $\displaystyle t=8$?
If you do the same for the bottom sequence, then you have two simultaneous equations. You need to solve these for $\displaystyle n$.

Re: Rate of increase
how could i be so thick grr thanks.