1. 5.6 Sum of Geometric Series (1/4)
Sn = for |r|>1
a(rn-1)
r-1
Term
Number
First
Term
Common
Ratio
Sum (add)
to n terms
Sn = for |r|<1
a(1-rn)
1-r

2. 5.6 Sum of Geometric Series (2/4)
Example:
Find the sum of the first 10 terms of …
a(rn – 1)
r - 1
r = 6÷2 = 3
Sn = since |3|>1
a = 2
2x(310 – 1)
3 - 1
S10 =
n = 10 =

3. 5.6 Sum of Geometric Series (3/4)
Example:
Evaluate … + 486
Find n
Find Sn
a(rn – 1)
r - 1
r = 6÷2 = 3
Tn = a rn – 1
Sn = since |3|>1
a = 2
486 = 2x3n – 1
2x(36 – 1)
3 - 1
Tn = 486
3n – 1 = 243
S6 =
log33n – 1 = log3243
= 728
n - 1 = log3243
ln 243
ln 3
n - 1 =
n – 1 = 5
n = 6

4. 5.6 Sum of Geometric Series (4/4)
Example:
Evaluate
a(rn – 1)
r - 1
Sn = since |3|>1
9x(36 – 1)
3 - 1
S6 =
a = 9
r = 3
n = 6
= 9837