Common Differences of Sequences and Series

[CrazCo]

Tn = 3/4n^2 -9

 

what is the common difference of said series/sequence

 

 

the answer is 3/2 and i dont know how it is.

 

 

i thought common different was just what each term differs by so i replaced n with numbers to get

 

t1=-8.25

t2= -6

t3= -2.25

 

 

and i dont see anything common. guidance?

[D H]

guidance?

http://www.purplemath.com/modules/nextnumb2.htm

Let me know if that answers your questions.

[CrazCo]

sort of, but it more so was the stuff i already know about common difference.

 

the specific sequence above is what i dont get

[D H]

You keep taking differences until you arrive at a common term. This will always happen for any series that can be expressed as a polynomial. The first differences for the series at hand are

 

[math]\Delta_1 t_n \equiv t_{n+1} - t_n = (3/4(n+1)^2 -9) - (3/4n^2 -9) = 3/2n+3/4[/math]

 

That's not constant, so take the second difference:

 

[math]\Delta_2 t_n \equiv \Delta_1 t_{n+1} - \Delta_1 t_n[/math]

 

This is constant, so the result is your common difference.

[CrazCo]

ohhhh

 

so linear you go to the first difference, quadratic you go to the second difference, and cubic the third

 

 

i feel so dumb now! thanks!