Geometric sequence and series 10
- 1. 10.19.20
- 2. 1. O T T F F S S E N _? T E F S 2. R O Y G B I _? T U V W
- 3. 1. 2, 4, 8, 16, 32, _? 6064 2. 3, -9, 27, _? 81 -81
- 4. 1. 2, 8 r = 𝟖 𝟐 r = 4 2. -3, 9 r = 𝟗 −𝟑 r = -3
- 5. A sequance is GEOMETRIC if there exist a number r, called common ratio.
- 6. 1). 1, 2, 4, 8, . . . r = 𝟐 𝟏 r = 2 2). 80, 20, 5, . . . r = 𝟐𝟎 𝟖𝟎 r = 𝟏 𝟒 The next term is 16 since 8(2) = 16. The next term is 𝟓 𝟒 since 5( 𝟏 𝟒 ) = 𝟓 𝟒 .
- 9. r = 𝟐𝟏 𝟕 r = 𝟑 𝒂9 = 𝟒𝟓, 𝟗𝟐𝟕
- 10. r = 𝟏𝟐 𝟑 r = 𝟒 192 768 192 768
- 11. r = 𝟔𝟒 𝟑𝟐 r = 𝟐 16 8 8 16
- 12. During the initial phase of an outbreak of measles, number of infections can grow geometrically. If there were 4, 8, 16, . . . On the first three days of an outbreak measles, how many will be infected on the 6th day?
- 13. r = 𝟖 𝟒 r = 𝟐 𝒂 𝒏 = 𝟒 n = 𝟔 128
- 14. In your book answer
- 15. 10.26.20
- 16. It is a sum of a geometric sequence.
- 17. r = 𝟏𝟔 𝟔𝟒 r = 𝟏 𝟒 256 3 𝒂 𝟏 = 𝟔𝟒
- 18. r = 𝟏 𝟗 𝟏 𝟑 r = 𝟏 𝟑 4 3 𝒂 𝟏 = 𝟏 𝟑 r = 𝟏 𝟗 • 𝟑 𝟏 r = 𝟑 𝟗
- 19. r = −𝟏 −𝟒 r = 𝟏 𝟒 − 16 3 𝒂 𝟏 = −𝟒
- 20. r = 𝟐 𝟏 r = 𝟐 The sum does not exist since 𝐫 > 𝟏. = 𝟏. 𝟒𝟏
- 21. r = 𝟗 𝟑 r = 𝟑 The sum does not exist since 𝐫 > 𝟏.
- 22. r = 𝟐 𝟗 − 𝟐 𝟑 r = − 𝟏 𝟑 𝑌𝑒𝑠, 𝑠𝑖𝑛𝑐𝑒 𝑟 < 1. r = 𝟐 𝟗 • − 𝟑 𝟐
- 23. It is a sum of a geometric sequence.
- 24. 𝒊𝒇 𝒓 = 𝟏, 𝒕𝒉𝒆𝒏 𝑺 𝒏 = 𝒏𝒂 𝟏. 2+2+2+2+2+2+2+2+2+2= 10(2) = 20 Solution:
- 25. r = −𝟏 n is even 𝑺 𝟏𝟎 = 𝟎
- 26. r = −𝟏 n is odd 𝑺 𝟏𝟏 = 𝟐
- 27. r = 𝟔 𝟑 = 𝟐 𝑺 𝟓 = 𝟗𝟑 Solution:
- 28. 4(0.4) = 1.6 ↑ 4𝑚 + ↓ 4𝑚 = 8𝑚 ↑ 1.6𝑚 + ↓ 1.6𝑚 = 3.2𝑚 ↑ 0.64𝑚 + ↓ 0.64𝑚 = 1.28𝑚 1.6(0.4) = 0.64
- 29. r = 𝟑.𝟐 𝟖 = 𝟎. 𝟒𝒎 𝑺 𝟓 = 𝟏𝟑. 𝟏𝟗𝟔𝟖 Solution: 𝑺 𝟓 = 𝟏𝟑. 𝟐𝟎𝒎
- 30. 10.23.20
- 31. The geometric mean between any two positive numbers a and b is the square root of their product.
- 32. 4 and 25 -3 and -12 𝑮𝑴 = 𝟏𝟎 𝑮𝑴 = 𝟔
- 33. 5, ____, ____, ____, 1280 = 𝟖𝟎= 𝟐𝟎 = 𝟑𝟐𝟎 20 80 320
- 34. 16, ____, ____, ____, 81 = 𝟑𝟔= 𝟐𝟒 = 𝟓𝟒 24 36 54
- 36. 7, ____, ____, 875 𝒓 = 𝟓 𝟑𝟓 35 175 𝟏𝟕𝟓
- 37. In your book answer