Algebra 2 GEOMETRIC SEQUENCES Geometric Sequences Algebra 2

Algebra 2 GEOMETRIC SEQUENCES

Geometric Sequences Algebra 2 The ratio between consecutive terms is a constant. This constant ratio is called the common ratio (r).

Geometric Sequences Lesson 11 -3 Algebra 2 Additional Examples Is the given sequence geometric? If so, identify the common ratio. a. 1, – 6, 36, – 216, . . . 1, – 6, – 6 36, – 6 – 216 – 6 ÷ 1 = – 6 36 ÷ – 6 = – 6 216 ÷ 36 = – 6 There is a common ratio of – 6. This is a geometric sequence.

Geometric Sequences Lesson 11 -3 Algebra 2 Additional Examples (continued) b. 2, 4, 6, 8, . . . 2, 4, 2 4÷ 2=2 6, 43 32 6÷ 4= 8 3 2 8÷ 6= 4 3 There is no common ratio. This is not a geometric sequence.

Geometric Sequence Formula Algebra 2

Geometric Sequences Lesson 11 -3 Algebra 2 Additional Examples Suppose you have equipment that can enlarge a photo to 120% of its original size. A photo has a length of 10 cm. Find the length of the photo after 5 enlargements at 120%. You need to find the 6 th term of the geometric sequence 10, 12, 14. 4, . . . an = a 1 • r n – 1 Use the explicit formula. a 6 = 10 • 1. 206 – 1 Substitute a 1 = 10, n = 6, and r = 1. 20. = 10 • 1. 205 24. 883 Simplify the exponent. Use a calculator. After five enlargements of 120%, the photo has a length of about 25 cm.

Geometric Mean Algebra 2

Geometric Sequences Lesson 11 -3 Algebra 2 Additional Examples A family purchased a home for $150, 000. Two years later the home was valued at $188, 160. If the value of the home is increasing geometrically, how much was the home worth after one year? geometric mean = = 150, 000 • 188, 160 Use the definition. 28, 224, 000 Multiply. = 168, 000 Take the square root.

Geometric Sequences Lesson 11 -3 Algebra 2 Lesson Quiz Is the given sequence geometric? If so, identify the common ratio and find the next two terms. 1. 1, 2, 6, 12, . . . no 2. 2, 1, 0. 5, 0. 25, . . . yes; 0. 5; 0. 125, 0. 0625 3. – 9, 81, – 729, 6561, . . . yes; – 9, – 59, 049, 531, 441 4. Write the explicit formula for the geometric sequence for which a 1 = 7 and r = 1. Then generate the first five terms. 3 an = 7 • 1 3 n– 1 ; 7, 7 7 , , , 3 9 27 81 5. Find the missing term for the geometric sequence 3, 12 , 48. . .