SeriesCh. 13

A series is an indicated sum of the terms of a sequence.

Finite sequence: 2, 4, 6, 8Finite series: 2+ 4 + 6 + 8 = 20

Infinite sequence: 2, 4, 6, 8, 10, …..Infinite series: 2 + 4 + 6 + 8 + 10 + …

Series

Sn indicates the sum of the first n terms of the series.

S12 means to add up the first 12 terms of the series.

S100 means to add up the first 100 terms of the series.

Sn

Find the sum of the first 50 terms of the arithmetic series 11 + 14 + 17 + 20+ ….

Sum of a Finite Arithmetic Series

1( )

2n

n

n t tS

Find the sum of the first ten terms of2 – 6 + 18 – 54 + …..

Sum of a Finite Geometric Series

1(1 )

1

n

n

t rS

r

1. Find S10 of the arithmetic series if:

t1 = 3 and t10 = -206.

2. S20 if 5 + 10 + 15 + 20 + …….

Problems

1. Find S10 if 1 + .5 + .25 + .125 + …..

2. Find Sn if, a1 = -3, an = -786432, r = 4

Problems #2

1. Find the number of terms in the arithmetic series if:

t1 = 7, tn = -91, Sn = -2100

2. Find the number of term in the geometric series if:

a1 = 6, r = -2, Sn = -8190

Problems #3