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we need to find n-th term formula, so first find differences
................................
.......................................
................................................
if we look at the second difference they go up in steps of
the next number in second row is
the next number in first row is
since second differences are equal, we conclude this is a quadratic sequence
n-th term formula is:
to find divide second difference by
now we have
substitute and in formula above to get formulas for first two terms
so, we have
use first two terms
............1) ............2)
----------------------subtract 1) from 2)
go to
............1), substitute
and your formula is:
now check if is in the sequence
...........solve for , the number of that term
...........simplify
........using quadratic formula we get
or
disregard negative solution, so
and th term is
