Geometric Sequences and Series it is for
- 1. Geometric Sequences and Series
- 2. 1, 4, 7,10,13 9,1, 7, 15 6.2, 6.6, 7, 7.4 , 3, 6 Arithmetic Sequences ADD To get next term 2, 4, 8,16, 32 9, 3,1, 1/3 1,1/ 4,1/16,1/ 64 , 2.5 , 6.25 Geometric Sequences MULTIPLY To get next term Arithmetic Series Sum of Terms 35 12 27.2 3 9 Geometric Series Sum of Terms 62 20/3 85/ 64 9.75
- 3. • Geometric Sequence: sequence whose consecutive terms have a common ratio. • Example: 3, 6, 12, 24, 48, ... • The terms have a common ratio of 2. • The common ratio is the number r. • To find the common ratio you use an+1 ÷ an
- 4. Vocabulary of Sequences (Universal) 1 a First term n a nth term n S sum of n terms n number of terms r common ratio
- 5. Find the next two terms of 2, 6, 18, ___, ___ 6 – 2 vs. 18 – 6… not arithmetic 2, 6, 18, 54, 162 Find the next two terms of 80, 40, 20, ___, ___ 40 – 80 vs. 20 – 40… not arithmetic 80, 40, 20, 10, 5
- 6. Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 – 2 vs. 9/2 – 3… not arithmetic 3 9/ 2 3 1.5 geometric r 2 3 2 9 2, 3, , , 27 81 243 4 8 , 2 16 Find the next two terms of -15, 30, -60, ___, ___ 30 – -15 vs. -60 – 30… not arithmetic -15, 30, -60, 120, -240
- 7. 1 a First term n a nth term n S sum of n terms n number of terms r common ratio -3 an 8 NA -2 n 1 n 1 a a r Find the 8th term if a1 = -3 and r = -2.
- 8. 1 a First term n a nth term n S sum of n terms n number of terms r common ratio ?? an 10 NA 3 n 1 n 1 a a r Find the 10th term if a4 = 108 and r = 3. 4
- 9. Write an equation for the nth term of the geometric sequence 3, 12, 48, 192, … 3 4 1 a First term r common ratio n 1 n 1 a a r
- 10. Geometric Mean: The terms between any two nonconsecutive terms of a geometric sequence. Ex. 2, 6, 18, 54, 162 6, 18, 54 are the Geometric Mean between 2 and 162
- 11. Find two geometric means between –2 and 54 -2, ____, ____, 54 1 a First term n a nth term n S sum of n terms n number of terms r common ratio -2 54 4 NA r n 1 n 1 a a r The two geometric means are 6 and -18, since –2, 6, -18, 54 forms a geometric sequence
- 12. Geometric Series: An indicated sum of terms in a geometric sequence. Example: Geometric Sequence 3, 6, 12, 24, 48 VS Geometric Series 3 + 6 + 12 + 24 + 48
- 13. Recall Vocabulary of Sequences (Universal) 1 a First term n a nth term n S sum of n terms n number of terms r common ratio
- 14. 1 a First term n a nth term n S sum of n terms n number of terms r common ratio 3 10 Sn NA Find the sum of the first 10 terms of the geometric series 3 - 6 + 12 – 24+ … -2
- 15. In the book Roots, author Alex Haley traced his family history back many generations to the time one of his ancestors was brought to America from Africa. If you could trace your family back 15 generations, starting with your parents, how many ancestors would there be? 1 a First term n a nth term n S sum of n terms n number of terms r common ratio 2 15 Sn NA 2
- 16. 1 a First term n a nth term n S sum of n terms n number of terms r common ratio a1 8 39,360 NA 3
- 17. 1 a First term n a nth term n S sum of n terms n number of terms r common ratio 15,625 ?? Sn -5
- 18. Recall the properties of exponents. When multiplying like bases add exponents
- 19. 1 a First term n a nth term n S sum of n terms n number of terms r common ratio 15,625 ?? Sn -5