Posted by Amy on Monday, October 11, 2010 at 6:36pm.
S(1)=3
S(2)=6
S(3)=11
S(4)=18
We note that S(2)-S(1)=6-3=3
S(3)-S(2)=11-6=5
S(4)-S(3)=18-11=7
Thus the difference increases uniformly. This is an indication that term n is related to the square of the number of terms, n.
Try
S(1)-1²=3-1=2
S(2)-2²=6-4=2
S(3)-3²=11-9=2
S(4)-4²=18-16=2
So the hypothesis that S(1) is related to the square of n is true, namely
S(n)=n²+2
So figure out which answer is correct.
For 3, 5, 7 increases by 2
so in the equation this is (+2)
or is does that mean that n is squared?
and S(1)-1²=3-1=2
S(2)-2²=6-4=2
S(3)-3²=11-9=2
S(4)-4²=18-16=2 this determines that it is (+2)in the equation?
or the other way around?
S(4)-4²=2
or
S(4)=4²+2, and in general,the rule is:
S(n)=n²+2
Check for cases n=2,3 and 4.
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