Question

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? (NOTE: This is an example of a mathematical series)

Answer 1

242

Explanation:

Given that two students start a club the first week of school. Each member invites three new members the second week of school.

Since each new member invites 3 additional members the following week, we have

I week = 2 students

II week= 2x3 +2 = 8 students( 2 old and 6 new)

III week = 8+6x3 = 26 students (8 old + 18 new)

Iv week = 26+18x3 = 80

V week = 80+54x3 = 242

Note: Note that new members invite 3 addl members already one week old members will not bring new additions.

Answer 2

In week 5, there will be 162 members already.

Let n = the week number and x = number of members, each week, let x be multiplied by 3. The series can be seen below:
n = 1, x = 2
n = 2, x = 6
n = 3, x = 18
n = 4, x = 54
n = 5, x = 162

Thank you for posting your question. I hope you found you were after. Please feel free to ask me another.