Arithmetic and geometric series

To find the sum of # terms of a geometric series use: Sn=t1(1-r^n)/1-r To find the sum of the # terms of an arithmetic series use: Sn=n(t1+tn)/2 A series is  a list of numbers that are added together. Example 1: 1)  Find the sum of the first 30 terms of 5 + 9 + 13 + 17 + . . . n = 30, that's pretty obvious! t1 = 5, and that's pretty obvious! We need the 30th term. Use the defintion of an arithmetic sequence. t30 = 5 + 29.4  = 121 So... S30 = 30(5 + 121)/2 = 1890 Example 2: {1,2,4,8,...} The sequence starts at 1 and doubles each time, so a=1 (the first term) r=2 (the "common ratio" between terms is a doubling) So we would get: {a, ar, ar2, ar3, ... } = {1, 1×2, 1×22, 1×23, ... } = {1, 2, 4, 8, ... } Example 3:  10, 30, 90, 270, 810, 2430, ... This sequence has a factor of 3 between each number. The values of a and r are: a = 10 (the first term) r = 3 (the "common ratio") The Rule for any term is: xn = 10 × 3(n-1) So, the 4th term would be: x4 = 10×3(4-1) = 10×33 = 10×27 = 270 And the 10th term would be: x10 = 10×3(10-1) = 10×39 = 10×19683 = 196830