Ray's New Higher Algebra : Elements of Algebra for Colleges, Schools, And Private Students

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Hence, Rule for finding the Sum of an Arithmetical Series. — Multiply half the sum of (he two extremes by the number of terms.
It also appears that The sum of the extremes is equal to the svm of any other two terms equally distant from the extremes.
S04. The equations ?=a+(»i — l)c7, and ^:=(a-\-l)-^, lurnish the means of solving this general problem : Knowing any three of the five quantities, a, d, I, n, S, ■which enter into an arithmetical series, to determine the other two.
The following tab
...le contains the results of the solution of all the diiferent cases. As, however, it is not possible to retain these in 256 RAY'S ALGEBRA, SECOND BOOK.
the memory, it is best, in ordinary cases, to solve all examples itt Arithmetical Progression by the above two formulaj: 0.
10.
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IG.
17.
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20, a, d, n a, d, S n, n, S d, n, S a, d, n a, d, I a, n, I d, n, I a, 71, I a, n, S a, I, S n, I, S a, d, I a, d, S a, I, S d, I, S d, 11, I d, n, S d, I, S n, I, S Ruquireil.
=a-\-[n—l)d, =-id±,/|2dS+(a-:irfr}, 2S S (n— l)d '7.


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