Sums of arithmetic and geometric series

13-3 sums of arithmetic and geometric series

A series is a list of numbers that are added together.

ex: 2 + 4 + 6 + 8..

-To find the sum of the __ terms of an arithmetic series, use this formula:

sn= n(t1 + tn)/2

-To find the sum of the __ terms of a geometric series, use this formula:

sn= t1(1-r^n)/1-r

Ex problem 1:

Find the sum of the first 10 terms of the geometric series.

2 - 6 + 18 - 54 +

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

S10= -29524

Ex problem 2: All multiples of 4 between 2 and 75

4, 8 … + 72

tn= t1 + n-1 (d)

72= 4 + (n-1)4

72= 4+4n-4

The 4 and (-4) cancel out, leaving you with 72=4n.

Solve for n by dividing 72 by 4 and your answer is n=18