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**11.3: Geometric Sequences & Series**

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1)

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1) Ex. 2 Determine the following: a) Find the eighth term of a geometric sequence for which a1 = -3 and r = -2.

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1) Ex. 2 Determine the following: a) Find the eighth term of a geometric sequence for which a1 = -3 and r = -2.

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1) Ex. 2 Determine the following: a) Find the eighth term of a geometric sequence for which a1 = -3 and r = -2. a8 = a1r(8 – 1)

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1) Ex. 2 Determine the following: a) Find the eighth term of a geometric sequence for which a1 = -3 and r = -2. a8 = a1r(8 – 1) a8 = (-3)r(8 – 1)

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1) Ex. 2 Determine the following: a) Find the eighth term of a geometric sequence for which a1 = -3 and r = -2. a8 = a1r(8 – 1) a8 = (-3)r(8 – 1) a8 = (-3)(-2)(8 – 1)

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1) Ex. 2 Determine the following: a) Find the eighth term of a geometric sequence for which a1 = -3 and r = -2. a8 = a1r(8 – 1) a8 = (-3)r(8 – 1) a8 = (-3)(-2)(8 – 1) a8 = (-3)(-27)

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1) Ex. 2 Determine the following: a) Find the eighth term of a geometric sequence for which a1 = -3 and r = -2. a8 = a1r(8 – 1) a8 = (-3)r(8 – 1) a8 = (-3)(-2)(8 – 1) a8 = (-3)(-27) a8 = (-3)(-128)

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**nth Term of an Geometric Sequence:**

an = a1r(n – 1) Ex. 2 Determine the following: a) Find the eighth term of a geometric sequence for which a1 = -3 and r = -2. a8 = a1r(8 – 1) a8 = (-3)r(8 – 1) a8 = (-3)(-2)(8 – 1) a8 = (-3)(-27) a8 = (-3)(-128) a8 = 384

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, …

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … 12 3

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … ·4

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1)

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)r(n – 1)

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)(4)(n – 1)

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3.

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: an = a1r(n – 1)

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1)

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1)

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1)

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1

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**b) Write an equation for the nth term of the**

b) Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … r = 4 an = a1r(n – 1) an = (3)4n – 1 c) Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1

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**c)Find the tenth term of a geometric**

c)Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1 2. Now use a1 = 4 and r = 3 to find a10

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**c)Find the tenth term of a geometric**

c)Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1 2. Now use a1 = 4 and r = 3 to find a10 an = a1r(n – 1)

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**c)Find the tenth term of a geometric**

c)Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1 2. Now use a1 = 4 and r = 3 to find a10 an = a1r(n – 1) a10 = a1r(10 – 1)

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**c)Find the tenth term of a geometric**

c)Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1 2. Now use a1 = 4 and r = 3 to find a10 an = a1r(n – 1) a10 = a1r(10 – 1) a10 = (4)r(10 – 1)

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**c)Find the tenth term of a geometric**

c)Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1 2. Now use a1 = 4 and r = 3 to find a10 an = a1r(n – 1) a10 = a1r(10 – 1) a10 = (4)r(10 – 1) a10 = (4)(3)(10 – 1)

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**c)Find the tenth term of a geometric**

c)Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1 2. Now use a1 = 4 and r = 3 to find a10 an = a1r(n – 1) a10 = a1r(10 – 1) a10 = (4)r(10 – 1) a10 = (4)(3)(10 – 1) a10 = (4)(39)

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**c)Find the tenth term of a geometric**

c)Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1 2. Now use a1 = 4 and r = 3 to find a10 an = a1r(n – 1) a10 = a1r(10 – 1) a10 = (4)r(10 – 1) a10 = (4)(3)(10 – 1) a10 = (4)(39) a10 = (4)(19,683)

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**c)Find the tenth term of a geometric sequence for**

c)Find the tenth term of a geometric sequence for which a4 = 108 and r = 3. 1. Find a1: a4 = a1r(4 – 1) 108 = a1r(4 – 1) 108 = a13(4 – 1) 108 = a133 108 = 27a1 4 = a1 2. Now use a1 = 4 and r = 3 to find a10 an = a1r(n – 1) a10 = a1r(10 – 1) a10 = (4)r(10 – 1) a10 = (4)(3)(10 – 1) a10 = (4)(39) a10 = (4)(19,683) a10 = 78,732

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r Ex. 3 Find the sum of the first 15 terms of the geometric sequence in which a1 = 2 and r = 2.

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r Ex. 3 Find the sum of the first 15 terms of the geometric sequence in which a1 = 2 and r = 2.

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r Ex. 3 Find the sum of the first 15 terms of the geometric sequence in which a1 = 2 and r = 2. S15 = a1(1 – r15)

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r Ex. 3 Find the sum of the first 15 terms of the geometric sequence in which a1 = 2 and r = 2. S15 = a1(1 – r15) S15 = 2(1 – r15)

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r Ex. 3 Find the sum of the first 15 terms of the geometric sequence in which a1 = 2 and r = 2. S15 = a1(1 – r15) S15 = 2(1 – r15) S15 = 2(1 – 215) 1 – 2

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r Ex. 3 Find the sum of the first 15 terms of the geometric sequence in which a1 = 2 and r = 2. S15 = a1(1 – r15) S15 = 2(1 – r15) S15 = 2(1 – 215) 1 – 2 S15 = 2(1 – 215) = 2(1 – 32,768) 1 –

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r Ex. 3 Find the sum of the first 15 terms of the geometric sequence in which a1 = 2 and r = 2. S15 = a1(1 – r15) S15 = 2(1 – r15) S15 = 2(1 – 215) 1 – 2 S15 = 2(1 – 215) = 2(1 – 32,768) = -65,534 1 –

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**Sum of a Geometric Series**

The sum Sn of the first n terms of a geometric series is given by the following: Sn = a1(1 – r n) 1 – r Ex. 3 Find the sum of the first 15 terms of the geometric sequence in which a1 = 2 and r = 2. S15 = a1(1 – r15) S15 = 2(1 – r15) S15 = 2(1 – 215) 1 – 2 S15 = 2(1 – 215) = 2(1 – 32,768) = -65,534 = 65,534 1 –

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{ 12.3 Geometric Sequence and Series SWBAT evaluate a finite geometric series SWBAT evaluate infinite geometric series, if it exists.

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