Sequence+&+Series+Project+Katie+M.

Arithmetic

Term 1=5: Term 2=7: Term 3=9: Term 4=11:

Recursive Formula: A n =A n- 1 +2 A 1 =5 Function Rule: A(n)=2n+3 A(50)= 103 A(50)=2(50)+3=100+3=103 Sum of Terms 1-20: 480 A(20)=2(20)+3=40+3=43 (n(t 1 + t n ))/2 = (20(5+43))/2 = (20(48))/2 = 960/2 = 480 Sum of Terms 15-28: 644 A(15)=2(15)+3=30+3=33 A(28)=2(28)+3=56+3=59 (n(tx+ty))/2 = (14(33+59))/2 = (14(92))/2 = 1288/2 = 644

Geometric

Term 1=3:

Term 2=6:

Term 3=12:

Term 4=24:

Recursive Formula: G n =2G n -1 G 1 =3 Function Rule: G(n)=1.5(2^n) G(50)= 1.689*10^15 G(50)=1.5(2^50)=1.5(1.126*10^15)=1.689*10^15 Sum of Terms 1-20: 3145728 (t1(r^n-1))/(r-1) = (3(2^20-1))/2-1 = (3(1048576-1))/1 = 3(1048575) = 3145728 Sum of Terms 15-28: 805257216 G(15)=1.5(2^15)=1.5(32768)=49152 (t x (r^n-1))/(r-1) = (49152(2^14-1))/(2-1) = 49152(16384-1)/1 = 49152( 16383)=805257216