Question 739620: general term formula for 1 5 14 28 47 please help me
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! This is similar to this problem
There's a lot of work and steps. Unfortunately I don't have the time right now to show them, so here is the answer:  where n is a positive integer.
Note: the answer with fractions only is 
Hopefully you can follow the work shown on the link I gave you. Then you can use that example to do this problem. I provided the answer as a check so you can be sure you are on the right page.
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! start with
n=1, 2, 3, 4, 5
to get
1 5 14 28 47 set pairs ( , )
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find a line which contains these points
 plug in first pair
 .......eq.1
plug in second pair
 ......eq.2
plug in third pair
 ......eq.3
you have a system:
.......eq.1
......eq.2
......eq.3
______________
.......eq.1...solve for 
 .....plug in eq.2
 ......eq.2
 .......solve for 
......eq.3...substitute and
since  , substitute
 .......solve for 
now find
and find
so,
since we are looking for general term  , set 
 ....your general term formula where  =,,.......
check: 
and so on.......
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