Question

What is the sum of the arithmetic series below?

Answer 1

\[\sum_{i=1}^{18}=2i+1\]

Answer 2

http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

Answer 3

=2(1+2+3....+18)+(1+1+1...18times)
=2(18*19/2)+18
=342+18
=360

Answer 4

One way to figure out the sums of arithmetic sequence is to find the mean value of the sequence then multiply the mean/average by the number of terms in the sequence.

1 3
2 5
3 7
4 9
5 11
6 13
7 15
8 17
9 19
10 21
11 23
12 25
13 27
14 29
15 31
16 33
17 35
18 37

The mean is 20 which you can see by adding the 1st and last term and dividing by two (or the 2nd and 17th, or the 9th and 10th).

Multiply 20 x 18 and you get 360 as the sum for the series.

Just a little shortcut.

Answer 5

Note: that you can only find the average/mean in this way in an arithmetic sequence. If the sequence isn't arithmetic, you would have to add all of the terms together and divide by 18.

Answer 6

if you use formula for arithmetic series (link attached above), all you need to find - first term (i=1) & the last one.
the answer is the same = 360
it just seems easier