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
.

8. r =
𝟖
𝟐
r =
𝟏
𝟐
=
𝟏
𝟔𝟒

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