# Rate of increase

• Jan 16th 2012, 10:00 AM
benjamin872
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)
• Jan 16th 2012, 10:13 AM
Quacky
Re: Rate of increase
You can do it by setting up an equation for the nth term of a sequence.

The "general term", $t$ of a sequence will be compared to the placement of the numbers in the sequence, $n$.

As sequence $1$ increases at a rate of $3$, $t=3n+k$, where $k$ is an unknown integer that we still need to work out. When $n=1$, $t=5$. Substituting this into the equation gives $5=3+k$, so $k=2$ and the equation I was looking for is $t=3n+2$. You can check this by substituting in the other numbers of the sequence. Ie, when $n$ is $2$, does $t=8$?

If you do the same for the bottom sequence, then you have two simultaneous equations. You need to solve these for $n$.
• Jan 16th 2012, 10:52 AM
benjamin872
Re: Rate of increase
how could i be so thick grr thanks.