Algebra 2: Sequences and series: Sum of an arithmetic series

Here is the link to the question.

http://www.flickr.com/photos/79746440@N0…

sum(i=1 to n)(3i - 2) =

3*sum(i=1 to n)(i) - 2*sum(i=1 to n)(1) =

3*n*(n+1)/2 - 2*n, so with n=15 the answer is 3*15*16/2 - 2*15 = 330.

Sum from i=1 to n=15 of (3i-2)
= (3 - 2) + (3*2 - 2) + (3*3 - 2) + .... (3*15 - 2)
= 3 + 3*2 + 3*3 + .... 3*15 - 2*15
= 3(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 +14 + 15) - 2*15
= 3(50 + 5 + 23 + 27 + 15) - 2*15
= 3(100 + 20) - 30
= 3(120) - 30
= 360 - 30 = 330

Instead of adding 1 + .... 15 you could find the average value... (15 + 1)/2 = 8 and multiplied it to 15.
8*15 = 120

(3*1-2)+(3*2-2)+(3*3-2)+(3*4-2)...(3*15-…

=3(1+2+3+4+..+15)-2*15
=360-30
=330