SOLUTION: 1 , 8 , 18 ... in the sequence above , the first term is 1 and the sum of the first n terms is equal to 3 to the power n for all n > 1 what is the fourth term in the sequence ?

Question 998671: 1 , 8 , 18 ...
in the sequence above , the first term is 1 and the sum of the first n terms is equal to 3 to the power n for all n > 1
what is the fourth term in the sequence ?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The sum of the first terms, and , is
.
The sum of the first terms, going all the way to , is
.
The sum of the first terms, going all the way to = the fourth term (to be found), is
must be .
So -->--> .

EXTRA:
If ,
then , and

All of that for , of course, as the problem specified.
For , the sum of the first terms is ,
which is not equal to .
That formula is how I mentally calculated ,
because is the type of calculation that I have hated to do since the first grade.
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