13-3

Section 13-3 was about finding the sum of a series. There are two formulas – one for geometric and one for arithmetic.

The sum of the first n terms of an arithmetic series:
Sn=n(t1+tn)/2

The sum of the first n terms of a geometric series:
Sn=t1(1-r^n)/1-r

Along with this section, there were a few terms we learned.
series: a list of numbers being added together
finite: a certain number
infinite: unlimited number of terms

EXAMPLE 1: Find the sum of the first 20 terms of the arithmetic series:
12 + 15 + 18 + 21 + 24..
A). This is an arithmetic series so we’re going to use the first formula.
B). Plug in your information given: S20=20(12 + t20)/2
C). We don’t know what t20 is, so we have find it by going back to what we learned in 13-1.
D). tn=12 + (20-1)3
E). By solving you find that t20=69. Now we can continue step B.
F). S20=20(12 + 69)/2
G). S20=810

EXAMPLE 2: How many multiples of 7 are there between 10 and 70?
A). Start off by figuring out the first few multiples: 7, 14, 21, 28.. and find the last one which is 63.
B). Now go back to 13-1 and use the formula tn=t1+(n-1)d
C). 63=7+(n-1)7
D). n=9