arithmetic and geometric sums of series

To find the sum of _terms of an arithmetic series
Sn = n(t1 + tn)/2

To find the sum of the _terms of a geometric series
Sn = t1(1 - r^n)/1 - r

Series – a list of numbers that are added together
2 + 4 + 6 + 8…



Example: Find the sum of all multiples of 4 between 2 and 75
72 = tn 4 = t1 4 = d
72 = 4 + (n - 1)(4)
72 = 4 + 4n – 4
72 = 4n 72/4 N =18
S18 = 18(4 + 72)/1
S18 = 1368/2
S18 = 684



Example: Find the sum of the first 25 terms of the arithmetic series
11 + 14 + 17 + 20… tn = t1 + (n - 1)d
tn = 11 + (25 - 1)(3)
tn = 83
S25 = 25(11 + 83)/2
S25 = 2350/2
S25 = 1175


Example: Find the sum of the first 100 terms of the arithmetic series
4 + 14 + 24…
tn = 4 + (100 - 1)(10)
tn = 994
S100 = 100(4 + 994)/2
S100 = 99800/2
S100 = 49900