Thread: 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?

You can do it by setting up an equation for the nth term of a sequence.

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

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

If you do the same for the bottom sequence, then you have two simultaneous equations. You need to solve these for .

how could i be so thick grr thanks.