Question 365094
Look for a pattern that looks like,
{{{X(n)=an^2+bn+c}}}
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Use the points to solve for {{{a}}},{{{b}}}, and {{{c}}}.
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1.{{{X[1]=a+b+c=4}}}
2.{{{X[2]=4a+2b+c=10}}}
3.{{{X[3]=9a+3b+c=18}}}
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Subtract eq. 1 from eq. 2,
{{{4a+2b+c-a-b-c=10-4}}}
4.{{{3a+b=6}}}
Subtract eq. 1 from eq. 3,
{{{9a+3b+c-a-b-c=18-4}}}
{{{8a+2b=14}}}
5.{{{4a+b=7}}}
Subtract eq. 4 from eq. 5,
{{{4a+b-3a-b=7-6}}}
{{{highlight(a=1)}}}
Then from eq. 4,
{{{3+b=6}}}
{{{highlight(b=3)}}}
Then from eq. 1,
{{{1+3+c=4}}}
{{{highlight(c=0)}}}
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{{{highlight_green(X(n)=n^2+3n)}}}