Two students start a club the first week of school. Each member invites three new members the second week of school. Each of these new members then invites three additional members the following week. If the pattern of each new member inviting three new members each week continues, how many members will be in the club after five weeks?
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Answer:
Initial students in 1st week N1 = 2
Each week only new members invites to 3 new members each.
Thus for second week new members invided N2 = N1 * 3
∴N2 = 2 × 3 =6
For 3rd week, new mwmbers invited N3 = N2 × 3
∴ N3 = 6 × 3 = 18
For 4th week, new mwmbers invited N4 = N3 × 3
∴ N4 = 18 × 3 = 54
For 5th week, new mwmbers invited N5 = N4 × 3
∴ N5 = 54 × 3 = 162.
Thus at the end of the 5th week, total members of the clube =Nt
Nt = N1 + N2 + N3 + N4 + N5
Nt = 2 + 6 + 18 + 54 + 162
Nt = 242
Answer: 242 members will be in the club after five weeks.
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