SOLUTION: Hi! I need some help developing a rule for the following number sequence: 4, 10, 18, 28, 40, 54, 72... I know that the pattern is increasing by two each time, but I am struggling

Algebra ->  Sequences-and-series -> SOLUTION: Hi! I need some help developing a rule for the following number sequence: 4, 10, 18, 28, 40, 54, 72... I know that the pattern is increasing by two each time, but I am struggling       Log On


   

Question 365094: Hi! I need some help developing a rule for the following number sequence: 4, 10, 18, 28, 40, 54, 72...
I know that the pattern is increasing by two each time, but I am struggling to find a rule for this pattern.
Any help would be appreciated!
Thanks!!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look for a pattern that looks like,
X%28n%29=an%5E2%2Bbn%2Bc
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Use the points to solve for a,b, and c.
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1.X%5B1%5D=a%2Bb%2Bc=4
2.X%5B2%5D=4a%2B2b%2Bc=10
3.X%5B3%5D=9a%2B3b%2Bc=18
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Subtract eq. 1 from eq. 2,
4a%2B2b%2Bc-a-b-c=10-4
4.3a%2Bb=6
Subtract eq. 1 from eq. 3,
9a%2B3b%2Bc-a-b-c=18-4
8a%2B2b=14
5.4a%2Bb=7
Subtract eq. 4 from eq. 5,
4a%2Bb-3a-b=7-6
highlight%28a=1%29
Then from eq. 4,
3%2Bb=6
highlight%28b=3%29
Then from eq. 1,
1%2B3%2Bc=4
highlight%28c=0%29
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highlight_green%28X%28n%29=n%5E2%2B3n%29