13-3 Sums of Arithmetic and Geometric

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…



Ex 1. 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


Ex 2. 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


Ex 3. Find the sum of the first 10 terms of the geometric series
2 - 6 + 18 - 54… To find r: -6/2 = -3 18/-6 = -3 r = -3

S10 = 2(1 - (-3)^10)/1 - (-3)
S10 = 2(1 - 59049)/4
S10 = -118096/4 = -29524



Ex 4. 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