# Khan/khan-exercises

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 Arithmetic series
randRangeNonZero(-40, 40) randFromArray([-1, 1]) * randRange(2, 6) randRange(5, 20) N * (2 * A + D * (N - 1)) / 2

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?

SUM

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).