1. Unit #4: Sequences & Series
Accel Precalc
Unit #4: Sequences & Series
Lesson #4: Infinite Geometric Sequences and Series
EQ: What is the formula to find the sum of an infinite geometric sequence?

3. ∞ 1 When the ratio is greater than 1, the
terms in the sequence will get _______ and _______.
larger
larger
If you add larger and larger numbers forever, you will get___ for an answer. ∞
So, we don't deal with infinite geometric series when the ratio is greater than ___. 1

4. 1 The ratio can't equal ___ because then the
series wouldn't be geometric (WHY?) and the sum formula would have division by ___.
The only case left, then, is when the ratio is ______ than 1.
less

5. List the first 10 terms for this sequence.
1/8 1
1/16
1/32
1/64
1/128
1/256
1/512
As the sequence goes on, the terms are getting ________ and ________, approaching ____.
smaller
smaller

6. 
So, if you replace rn with ___ in the summation formula, the 1 - rn part just becomes ____, and the numerator just becomes ____. 1 a1

7. Day 34 Agenda:
DG minutes

8. ***If |r| > 1, then finding the sum is NOT POSSIBLE!

9. 2.4
0.6

10. 0.1
0.01
0.001
.1 1
.1 2
.1 3
3(0.1)n-1
0.1 3

12. = …
= 5(0.1) + 5(0.01) + 5(0.001) + 5(0.0001) + …
= 5(0.1)1 + 5(0.1)2 + 5(0.1)3 + 5(0.1)4 + … OR

13. = …
= 47(0.01) + 47(0.0001) + 47( ) + …
= 47(0.01)1 + 47(0.01)2 + 47(0.01)3 + … OR

14. = …
= (0.1) + 0.6(0.01) + 0.6(0.001) +…
= (0.1) + 0.6(0.1) (0.1)3 +… OR
CHECK:

15. At --- P0 --- r --- n --- t --- Recall: final amount of money after t
P0 ---
r ---
n ---
t ---
final amount of money after t
initial amount of money; principle
annual interest rate (decimal)
times per year interest is calculated
total number of times interest is calculated

16. Ex. A deposit is made of $50 on the first day of each month in a savings account that earns 6% compounded monthly. What is the balance of this annuity at the end of 2 years?

17. Total Balance will be sum of the balances after
the 24 deposits.
Use the sum formula for a finite geometric series. 24
50(1.005)1
This is the LAST deposit made. It will earn interest for 1 month.

18. This account will have a balance of $1277.95 at the end of 2 years.
Ex. A deposit is made of $50 on the first day of each month in a savings account that earns 6% compounded monthly. What is the balance of this annuity at the end of 2 years?
This account will have a balance of $ at the end of 2 years.

19. Assignment: p ODDS #69 – 91