What is the sum of the arithmetic sequence 2, 4, 6, ..., 1880 ?

2 Answers
George C.
Dec 6, 2017

884540

Explanation:

The sum of an arithmetic sequence is the number of terms multiplied by the average term and the average term is the same as the average of the first and last terms.

In our example we can see that the number of terms is 940 by separating out a factor of 2, so:

2+4+6+...+1880 = 2 * (1+2+3+...+940)

color(white)(2+4+6+...+1880) = 2 * 940 * (1+940)/2

color(white)(2+4+6+...+1880) = 940 * 941

color(white)(2+4+6+...+1880) = 884540

Alexi De Avila Cadena
Dec 6, 2017

884540
Use a sigma sum series.

Explanation:

The pattern is n*2, for every n (some number) there is a two added to it.
For example:
0*2=0
1*2=2
2*2=4 etc.
If sum_(i=1)=n*2
which computes to be 884540
So if you do the amount of terms n and square by two (because the anti derivative of 2n is n^2) and add 940 you get your answer. int2n=n^2+c and c=940 because it is your amount of terms.
I remember it using calculus based integration, I am not sure what they taught you in Precalculus.

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