Question 933337: For each sequence, find a closed formula for the general term, a sub n.
1. 53,477,4293,38637,347733,... a sub n =
2. 2,5,10,17,26,...a sub n =
3. -2,-8,-18,-32,-50,...a sub n =
Help would truly be appreciated!
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! a sub n means the "nth" term of the sequence.
Example: 1,2,3,4,5,....,
the nth term is n. We say "a sub n = n"
Example 2: 1,4,9,16,25,...
We say "a sub n = n^2".
1. 53,477,4293,38637,347733,...
to get next term multiply previous one by 
a sub n = (for all terms given)
if n=0,1,2...
check:
or
 if n=1,2...
check:
:
:
I prefer this one because is better to have  as first term
2. 2,5,10,17,26,...
pattern
2---- 5---- 10---- 17---- 26,..
-- 3---- 5---- 7-- 9...............first diff
---- 2---- 2---- 2................second diff.; all  s, so degree is , half of it (or  )will be coefficient of 
use
 , set up system of three equations to find coefficients  , , and 
For instance, I know that the first term (that is, the term when n = 1) is , so I'll plug in for  and for the value:
The second term (that is, the term when  ) is 5, so:
The third term (that is, the term when  ) is  , so:
 .........1
 ...........2
 ...........3
___________________________
.........1
 ...plug in 2..........................a
 ...........2
 ...........................b
 ...........3...plug in a
 ......plug in b
find and :
so, we have  ,  , and  , and the formula is:
1n^2 + 0n + 1 = 
so, a sub n = (for all terms given)
3. -2,-8,-18,-32,-50,...a sub n =
-2 ---- -8 ---- -18---- -32 ---- -50
----..-6----..-10----..-14---..-18
---- .. -4---- .. -4---- .. -4.........third difference, -> 3rd degree; constant is -4, so half of it (or -2)will be coefficient of n^2
a sub n =  (for all terms given)
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