N2(squared) +2?

frist five terms in the sequence plz, i've worked it out but the gaps arent equal

Answers:
As the sequence is n^2 +2 the gaps are not supposed to be equal.

When you take the difference of these gaps, then they should be equal.

That hows you find out the nth sequence by taking gaps.

A linear sequence(n to the power of one) will have equal gaps though, eg n+2
1^2+2=3
2^2+2=6
3^2+2=11
4^2+2=18
5^2+2=27
are you back again?
we're doing your homework aren't we?..lol

1x1+2 = 3
2x2+2 = 6
3x3+2 = 11
4x4+2 = 18
5x5+2 = 27

they won't be if theres a squared in the equation.

when your given just numbers try extrapolating back

so pretend if you got given 3 6 11 18 27

difference is 3 5 7 9

extrapolate again... see the difference is 2.

then you know it's squared
Why *should* the gaps be equal?
if you look at my difference tables,you
will see that the gaps are not equal until
the second difference
thus indicating a second order polynomial
in n

if the gaps were not equal until the 3rd
difference you would have n in the
form of a 3rd order polynomial
namely, N=ax^3+bx^2+cx+d

i hope that this helps
n= 0,1,2,3,4,5
S= 2,3,6,11,18,27

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