SOLUTION: Give AP -7,-3,1,....,state three consecutive terms in this AP which sum up to 75

Algebra ->  Sequences-and-series -> SOLUTION: Give AP -7,-3,1,....,state three consecutive terms in this AP which sum up to 75      Log On


   

Question 828533: Give AP -7,-3,1,....,state three consecutive terms in this AP which sum up to 75
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In arithmetic progressions, given 3 term, the middle one is the average,
In other words, 3 consecutive terms add up to 3 times the middle term.
So, 75%2F3=25 is the middle term.
The common difference is 1-%28-3%29=1%2B3=4 ,
so the three terms are
25-4=highlight%2821%29 ,
highlight%2825%29 . and
25%2B4=highlight%2829%29 .

How do I know that the average of 3 terms is the middle term?
a%5Bn%5D=a%5Bn-1%5D%2Bd so a%5Bn-1%5D=a%5Bn%5D-d ,
and a%5Bn%2B1%5D=a%5Bn%5D%2Bd .
Adding them up you have
a%5Bn-1%5D%2Ba%5Bn%5D%2Ba%5Bn%2B1%5D=%28a%5Bn%5D-d%29%2Ba%5Bn%5D%2B%28a%5Bn%5D%2Bd%29
a%5Bn-1%5D%2Ba%5Bn%5D%2Ba%5Bn%2B1%5D=a%5Bn%5D-d%2Ba%5Bn%5D%2Ba%5Bn%5D%2Bd
a%5Bn-1%5D%2Ba%5Bn%5D%2Ba%5Bn%2B1%5D=a%5Bn%5D%2Ba%5Bn%5D%2Ba%5Bn%5D
a%5Bn-1%5D%2Ba%5Bn%5D%2Ba%5Bn%2B1%5D=3%2Aa%5Bn%5D