A school club uses a telephone chain to inform members of changes in plans. The club president calls 2 members, each of whom calls 2 members, and so on. The process must be repeated 5 times. How many members are in the club?

63 members

Step-by-step explanation:

Since each person calls 2 persons each, there is an exponential increase of 2 for each level. Since it starts with the president as 1 person, and increases exponentially by 2 for each level of phone call, we have a geometric progression of first term, a = 1 and common ratio r = 2. Since the process of phone calls must be repeated 5 times, our last term is 2⁵. So, our geometric progression is 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ = 1 + 2¹ + 2² + 2³ + 2⁴ + 2⁵

We now sum the geometric progression

The sum of a geometric progression with r > 1 is

S = a(rⁿ - 1)/(r - 1)

substituting r = 2, a = 1 and n = 6 since we have 6 terms, we have

S = 1(2⁶ - 1)/(2 - 1)

= (64 - 1)/1

= 63

So, we have 63 members in the club.

We could have also found this by summing up individually the terms in the series. We have 1 + 2¹ + 2² + 2³ + 2⁴ + 2⁵ = 1 + 2 + 4 + 8 + 16 + 32 = 63

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

me! what did you put for this question?

step-by-step explanation: