Help in trying to find the tenth term of the sequence. Will give MEDAL!

Question

calculusxy · Answer

7, 9, 12, 16, 21, ... 
@Directrix

welshfella · Answer

differences ar 2,3,4,5 ...

calculusxy · Answer

yeah but i just can't figure out the recursive formula.

welshfella · Answer

me neither i think theres  squared value in these types but cant remember..

calculusxy · Answer

can you help me figure out the pattern for this 

-6, -2, 0, 1, 3/2

welshfella · Answer

1/2 [ n^2 + n + 12]

welshfella · Answer

- that is  the first one.

calculusxy · Answer

omg that works!!

welshfella · Answer

yea if the differences are an arithmetic sequence then the formula is  an expression in x^2

calculusxy · Answer

i thought that that was with geometric sequences ?

welshfella · Answer

yes GP's also

welshfella · Answer

the differences are a G P_

4, 2 , 1 , 1/2...

calculusxy · Answer

so it's like dividing by 1/2

welshfella · Answer

no not as simple as that 
There will be a more complicated formula for this one

welshfella · Answer

No I cant think of a way to do this one

calculusxy · Answer

okay. i'll do that later then. 

what about -28, 172, 372, 572, 772

welshfella · Answer

I'm not chickening out but i have to go in 5 minutes..

welshfella · Answer

they are all multiples of 4    which might help

welshfella · Answer

so it might be
4( an - b)     where a and b are positive numbers  and b > a  to get the first number negative

welshfella · Answer

gtg

calculusxy · Answer

ok thanks for ur help :)