2. Accel PRecalc Unit #4: Sequences & Series Lesson #3: Finite Geometric Sequences and Series
EQ: What is the formula to find the sum of a finite geometric sequence?

3. Recall: Geometric Sequence
--- ordered list of numbers with a common ratio called r
Ex 1. Determine if each sequence is geometric.
Justify your answer.

4. Write the explicit formula for finding the nth term of a geometric sequence.
an = _________________
Ex 2. Write the explicit formula of the geometric sequence whose initial term is 3 and whose common ratio is 2. Then find the first five terms.
an = _________________
a1 = ___ a2 = ___ a3 = ___ a4 = ___ a5 = ___ 3 6 12 24 48

5. Ex 3. Write the explicit formula of the geometric sequence whose first term is a1 = 20 and has a common ratio of r = Then find the 15th term of the sequence.
39.599
an = _________________ a15 = ___

6. Ex 4. Write the explicit formula of the geometric sequence whose third term is a3 = 64 and whose seventh term is a7 = 16,384.
Calculate ratio:
16,384 ÷ 64 = 256
But this ratio is from a3 to a7.
Now find a1.
an = _________________

7. Geometric Sequences in Summation Notation
Recall: Summation Notation
But a geometric sequence is NOT LINEAR.
A geometric sequence is EXPONENTIAL.

8. Ex 5. Use summation to express each sum.
HINT:
Identify initial term
HOW?
r = an ÷ an-1
Calculate common ratio. … 5 15 5 3
a1 = _____ an = ______ an-1 =______ r = ___
r = 15 ÷ 5

9. How do we find the UPPER LIMIT?
RECALL:
Solve EXPONENTIALS using LOGS!!

10. Solve for upper limit using LOGS, but use ¼ NOT -¼.
a1 = _____ an = ______ an-1 =______ r = ___ 2
Solve for upper limit using LOGS, but use ¼ NOT -¼.
7 = n
Take log of both sides,
then divide.

11. Assignment:
p. 644 ODDS #1 - 41

13. Each consecutive term increases by a factor of r.
How to Find the Sum of a Finite Geometric Sequence:
Each consecutive term increases by a factor of r.

14. Solve for Sn

15. 12
(0.3)12
1.2
0.3
4(0.3)1

16. 5 6 2
(2)5
Be careful if the INDEX begins at i = 0. You will need to adjust the summation formula so that it BEGINS AT i = 1.
Ex.
WHY?
For the summation formula, the first term is a1, not a0.

17. You now know 2 formulas:
Summation for an Arithmetic Sequence
Summation for a Finite Geometric Sequence
These are NOT interchangeable and ONLY work for their SPECIFIC type of sequence.
Assignment:
p. 644 ODDS #