Question

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?

Answer 1

Answer:

6144 clients

Step-by-step explanation:

Number of clients in the beginning = 3

The 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:

$a_{n}=a_{1}(r)^{n-1}$

Here,

$a_{1}$ is the first term of the sequence which is 3

r 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:

$a_{12}=3(2)^{12-1}=6144$

Thus, after 1 year the company started by Nick will have 6144 clients