Question 1089382: Find the nth term for the following progression
8, 14, 22, 32, 44
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!  ,  ,  ,  , 
find differences:
....................................
..... ...................... .........
.............. ......................-> second differences are constant, the sequence can be described by a quadratic formula of the form:
now find coefficients  , , and 
To find the values of ,  and consider the first  terms.
Using  and  gives
 ..........eq.1
Using  and  gives
 ..........eq.2
Using  and  gives
 ..........eq.3
solve the system:
..........eq.1
..........eq.2
..........eq.3
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start with ..........eq.1 and solve for
 ..........eq.1a
same with ..........eq.2
 .........eq.2b
from eq.1a and eq.2b we have
 ................solve for
 ...........eq.3c
go to ..........eq.1a, substitute
 .........eq.4d
take eq3c and eq.4d, and substitute it in
..........eq.3
find ...........eq.3c
and .........eq.4d will be
so, the nth term for the following progression is:
 (for all terms given)
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