Question 969779: Find the 1st term of this arithmetic sequence, - 3 , 17
Answer by KMST(5328)   (Show Source):
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Are there any terms before 3?
If not, then 3 is the first term.
Is 3 the second term, and 17 the third term?
If it is an arithmetic sequence, then each term is the one before plus a fixed number,  .
That number is called the common difference, because it is the difference between any two consecutive terms.
So, term number  ,  ,
is related to the previous term,
term number  = ,
by  <--->
for all natural number (counting number) values of .
If 3 and 17 are the 2nd and 3rd terms respectively,
then the common difference between consecutive terms is
 .
Each term is  more than the one before.
 ,  ,  , and  is the first term that we want to find.
From , for  , we get
 ---> --->
so  ---> --->
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