The arithmetic sequence (a_i) is defined by the formula:
a_i = A + D(i - 1)
What is the sum of the first N terms in the series, starting with a_1?
The sum of an arithmetic series is the number of terms in the series times the average of the first and last terms.
To find the sum of the first N terms,
we'll need the first and ordinalThrough20(N) terms of the series.
a_1 = A + D (1 - 1) = A
a_{N} = A + D (N - 1) = A + D * (N - 1)
Therefore, the sum of the first N terms is
\qquad n\left(\dfrac{a_1 + a_{N}}{2}\right) = N \left(\dfrac{A + A + D * (N - 1)}{2}\right) = SUM.
a_1 = A
a_i = a_{i-1} + D
First, let's find the explicit formula for the terms of the arithmetic series. We can see that the first term is A and the common difference is D.
Thus, the explicit formula for this sequence is a_i = A + D(i - 1).