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Accel Math III
Unit #3: Sequences & Series
Lesson #3: Finite Geometric Sequences and
Series
MA3A9: Students will use sequences and series. b. Recognize and use simple arithmetic and geometric sequences. e. Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series. f. Use summation notation to explore series. g. Determine geometric series and their limits.
EQ: What is the formula to find the sum of a
finite geometric sequence?
Recall:
- Geometric Sequence --- ordered list of numbers with a common __________called _______
Ex 1. Determine if each sequence is geometric. Justify your answer.
a. 2, 8, 12, 48, 52, … b. -8, 4, -2, 1, …
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 = _________________
a 1 = ___ a 2 = ___ a 3 = ___ a 4 = ___ a 5 = ___
Ex 3. Write the explicit formula of the geometric sequence whose first term is a 1 = 20 and has a common ratio of r = 1.05. Then find the 15 th^ term of the sequence. an = _________________ a 15 = ___
- Identify initial term
- Calculate common ratio. HOW? r = an ÷ an-
Ex 5. Use summation to express each sum:
a. 5 + 15 + 45 + … + 3645
a 1 = _____ an = ______ an-1 =______ r = ___
b. -^ +^ -^ +
1 1 1 2 ... 2 8 2048
a 1 = _____ an = ______ an-1 =______ r = ___
How to Find the
Sum of a Finite Geometric Sequence:
GOAL: We are looking for Sn
- Begin with the Sum of an Infinite Geometric Sequence:
Sn = a 1 + a 1 r + a 1 r^2 + a 1 r^3 + … + a 1 rn-
2. Multiplying both sides by r:
WHY CAN YOU DO THIS?
rSn = a 1 r + a 1 r^2 + a 1 r^3 + a 1 r^4 … + a 1 rn-1+ a 1 rn
RECALL: SOLVING SYSTEMS OF EQUATIONS
- Subtracting these two equations:
Sn = a 1 + a 1 r + a 1 r^2 + a 1 r^3 + … + a 1 rn-
∑ (^ )
=
12
1
n
a. n
n = ____ a 1 = ______ r = ______ rn^ = ________
1 (^1 )
n
n
a r
S
r
− = _________________
b.
n = ____ a 1 = ______ r = ______ rn^ = ________
1 (^1 )
n
n
a r
S
r
− = _________________
Assignment: p. 644 ODDS #1 – 41, 55 - 67
