Question

Mr. Blue's first year salary is $30,000 and it doubles each year. What is the explicit rule for the sequence in simplified form?

Answer 1

Mr. Blue' salary is an illustration of a geometric sequence

• The explicit rule of Mr. Blue 's salary is an = 30000 * 2^(n - 1)
• The recursive rule of Mr. Blue's salary is an+1 = 2an; a1 = 30000

How to determine the explicit formula?

Mr. Blue's salary is a geometric sequence with the following parameters:

First term, a1 = 30000

Rate, r = 2

The explicit rule is calculated as:

an = a1 * r^(n - 1)

This gives

an = 30000 * 2^(n - 1)

How to determine the recursive formula?

The common ratio is calculated as:

r = an+1/an

Substitute 2 for r

2 = an+1/an

Cross multiply

an+1 = 2an

Hence, the recursive rule of Mr. Blue's salary is an+1 = 2an; a1 = 30000

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