# 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", \$\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\$.
• Jan 16th 2012, 10:52 AM
benjamin872
Re: Rate of increase
how could i be so thick grr thanks.