SOLUTION: Consider the sequence 6,6,2,-6,-18....show that -6838 is in the sequence

Question 1177330: Consider the sequence 6,6,2,-6,-18....show that -6838 is in the sequence
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

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

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