HOW DO YOU COME UP WITH EQUATIONS??

Question

Ok So my math teacher wants us to come up with an equation that when you INPUT the numbers 1, 2, 3,4, .... and so forth, the OUTPUT is 3, 8, 13, 18... and so forth.... anyone know any tips as to how to come up with equations where you can sub the nth term and find the output for the nth term?

How do you start to think of comeing up with these and what is the answer to this particulat one with the output being 3,8, 13,18? Thanks

Answer 1

When you get sequences like these, you look at the difference between the consecutive numbers.  You notice that in the sequence": 3, 8, 13..., the difference between consecutive numbers is 5- each number is 5 more than the number which comes before.  But:

5*1 = 5, 5*2 = 10, 5*3 = 15, 5*4 = 20...gives the sequence:

5, 10, 15, 20, 25...

While the sequence we have is:

3,  8,  13, 18, 23...

Notice that each number in the sequence is 2 less.

This means that the equation used for generating the sequence is:

5n - 2, where for n, you input 1, 2, 3, 4, 5 and so on.

Answer 2

ok see its going up by the same change of +5 each time.thats how u know u have a linear function

ok so u knwo the change is 5

so lets just presume we know that y=5x

lets test it with the first entry

we know that when x=1 y = 3

is that true for y=5x

no

how can we make it true

3= 5*1-2

ahah we have to subtract 2

so the equation is y = 5x-2