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A lesson from Accel Math III Unit #3 on Sequences & Series, focusing on Finite Geometric Sequences and Series. Students will learn to recognize and use simple arithmetic and geometric sequences, find sums of finite and infinite geometric series, and use summation notation to explore series. exercises to determine if sequences are geometric, find the nth term of a geometric sequence, and use summation notation to express sums.
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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.
Recall:
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 = ___
Ex 5. Use summation to express each sum:
a. 5 + 15 + 45 + … + 3645
b. -^ +^ -^ +
1 1 1 2 ... 2 8 2048
Sn = a 1 + a 1 r + a 1 r^2 + a 1 r^3 + … + a 1 rn-
Sn = a 1 + a 1 r + a 1 r^2 + a 1 r^3 + … + a 1 rn-
=
12
1
n
a. n
n
n
b.
n
n
Assignment: p. 644 ODDS #1 – 41, 55 - 67