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

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(39618) (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,
;

The description will give this system:

Some simplification,

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:

Dividing the second equation by the first equation gives
(because notice the four-term polynomial expression in both equations)

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