The starting salary at a company is $42,000 per year. The company automatically gives a raise of 3 % per year. Write the explicit and recursive formulas for the geometric sequence formed by the salary increase.
The starting salary at a company is $42,000 per year. The company automatically gives a raise of 3 % per year. Write the explicit and recursive formulas for the geometric sequence formed by the salary increase.
The starting salary at a company is $42,000 per year. The company automatically gives a raise of
3
%
per year. Write the explicit and recursive formulas for the geometric sequence formed by the salary increase.
Expert Solution & Answer
To determine
To write: the explicit and recursive formulas for the geometric sequence formed by the salary increase.
Explanation of Solution
Given Information: The starting salary $42,000 . The company automatically gives a raise of 3% per year.
Calculations:
Formula used: The nth term of a geometric sequence is given as follows
an=a1rn−1............(1)
Where a1 is the first term.
r is the common ratio.
Since, the starting salary at the company is $42,000 , therefore , a1=42,000 .
Calculations :
The company automatically gives the rise of 3% every year, therefore, a2=42,000+3%(42,000)
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