Raymond+D+Sequence+&+Series+Project


 * >Arithmetic**





U n-1 = U n-1 + 2 U 1 = 2

U (n) = 2 (n-1) + 2

U(50) = 2(49) +2 U(50) = 98 + 2 U(50) = 100

U(20) = 2(19)+2 U(20) = 38+2 U(20) = 40

n(a1+an)/2 20(2+40)/2 20(42)/2 840/2 =420

U(15) = 2(14) + 2 U(15) = 28+2 U(15) = 30

U(28) = 2(27) + 2 U(28) = 54+2 U(28) = 56

n(ax+ay)/2 14(30+56)/2 14(86)/2 1204/2 = 602


 * >Geometric **







U n = U n-1 X 2 U 1 = 3

U(n) = 3 X 2^n-1

U(50) = 3 X 2^49 U(50) = 3 X 5.629499534e14 U(50) = 1.68884986e15

t1 (r^n - 1)/r-1 3 (2^20 -1)/2-1 3 (1048576 - 1)/1 =3145725

U(15) = 3X 2^14 U(15) = 3X 16384 U(15) = 49152

U(28) = 3X 2^27 U(28) = 3X 134217728 U(28) = 402653184

49152 (2^14 - 1)/2-1 49152 (16384 - 1)/1 49152 (16383)/1 = 805306368