Question

Susan starts her own telemarketing company by recruiting 3 employees into what she calls Recruiting Group 1. She requires each employee in Recruiting Group 1 to recruit 3 additional employees for Recruiting Group 2. The employees in each successive recruiting group must meet the same requirement of recruiting 3 additional employees. Write the first 5 values of the following sequence starting with Group 1

Answer 1

The Number of employees in the first five groups expressed as a sequence is 3, 9, 27, 81 and 243

Number of employees = 3

Each employee in each group employs 3 employees into the next group.

• Taking the number group as n

The number of employees in each group can be obtained using the expression :

${3}^{n}$

For the first group, n = 1

• Number of employees = $3^{1} = 3$

For the second group, n = 2

• Number of employees = $3^{2} = 9$

For the third group, n = 3

• Number of employees = $3^{3} = 27$

For the fourth group, n = 4

• Number of employees = $3^{4} = 81$

For the fifth group, n = 5

• Number of employees = $3^{5} = 243$

The sequence of numbers representing the number of employees in the first five groups :

• 3, 9, 27, 81, 243

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