Nick recently started a landscaping company. He began with 3 3 clients. Thanks to word-of-mouth referrals, his clients double each month. How many clients will Nick have after one year?

Accepted Solution

Answer:6144 clients Step-by-step explanation:Number of clients in the beginning = 3The number of clients doubled each month. This means for every month the number of clients was 2 times the previous month. This can be modeled by a geometric sequence, with first term as 3 and common ratio of 2.The general formula for the geometric sequence is:[tex]a_{n}=a_{1}(r)^{n-1}[/tex]Here, [tex]a_{1}[/tex] is the first term of the sequence which is 3r is the common ratio which is 2 and n represents the number of term.We need to calculate the number of clients after 1 year i.e. after 12 months. So here n will be 12. Using these values, we get:[tex]a_{12}=3(2)^{12-1}=6144[/tex]Thus, after 1 year the company started by Nick will have 6144 clients