SOLUTION: the sum of the first and the last terms of a linear sequence (A.P) is 42. if the sum of all the terms is 420 and the second the is 4 . find the the number of terms,the common diffe

Algebra ->  Sequences-and-series -> SOLUTION: the sum of the first and the last terms of a linear sequence (A.P) is 42. if the sum of all the terms is 420 and the second the is 4 . find the the number of terms,the common diffe      Log On


   

Question 983043: the sum of the first and the last terms of a linear sequence (A.P) is 42. if the sum of all the terms is 420 and the second the is 4 . find the the number of terms,the common difference and the last term of the sequence.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This solution is not finished.
Using expression for general term of the sequence, A for first term, when n=1,
A%2B%28n-1%29d;

The description will give this system:
system%28A%2BA%2B%28n-1%29d=42%2C%28n%2F2%29%28A%2BA%2B%28n-1%29d%29=420%2CA%2Bd=4%29

Some simplification,
system%282A%2Bnd-d=42%2C%28n%2F2%29%282A%2Bnd-d%29=420%2CA%2Bd=4%29

system%282A%2Bnd-d=42%2Cn%282A%2Bnd-d%29=840%2Cd=4-A%29

Try substituting for d in the first two equations of this last form of the system....

... Working through the algebra steps for that brings to the system:
system%283A%2B4n-nA-4=42%2Cn%283A%2B4n-nA-4%29=840%29

Dividing the second equation by the first equation gives
(because notice the four-term polynomial expression in both equations)
n=840%2F42
highlight%28n=20%29

Review everything and try to understand, and then continue to find A and d.