Maths help?

if there is a sequence of 3, 7, 12, 18
what is the nth term?
Please help someone

 

from 3 to 7, the difference is 4
from 7 to 12, the difference is 5
from 12 to 18, the difference is 6.


I think I'm overthinking this problem. I'm not coming to the solution, sorry.

 

I believe it is 2.5n +.5n^2 but let me check it...

Yep, it's correct! The starting term is n = 1.

Work:
a + (n-1)d + .5(n-1)(n-2)i
a = first term
d = first difference
i = increase in differences

Applied to your problem,
3 + (n-1)4 + .5(n-1)(n-2)1
4 because 7-3 = 4, 1 because 7-3 = 4, 12-7 = 5, 18-12 = 6, so the common increase is simply 1.

I believe you can do the rest of the work and the proof.

 

Alex is correct, but 2.5n +.5n^2 can be simplified to:
A(n) = (n/2)*(n + 5)

~daswasup