Question 836844
<pre>
t(n) = an² + bn + c

t(1) = a(1)² +b(1) + c =  a +  b + c = 2
t(2) = a(2)² +b(2) + c = 4a + 2b + c = 5
t(3) = a(3)² +b(3) + c = 9a + 3b + c = 19

{{{system(a +  b + c = 2,4a + 2b + c = 5, 9a + 3b + c = 19)}}}

Solve that system and get a = {{{11/2}}}, b = {{{-27/2}}}, c = {{{10}}}

t(n) = an² + bn + c

t(n) = {{{expr(11/2)n^2-expr(27/2)n+10}}} 

t(1) = {{{expr(11/2)1^2-expr(27/2)1+10}}} = 2

t(2) = {{{expr(11/2)2^2-expr(27/2)2+10}}} = 5

t(3) = {{{expr(11/2)3^2-expr(27/2)3+10}}} = 19

t(4) = {{{expr(11/2)4^2-expr(27/2)4+10}}} = 44 = x

t(5) = {{{expr(11/2)5^2-expr(27/2)5+10}}} = 80 = y

Edwin</pre>