![]() Thus, the salary for the fifth month that we previously calculated using the recursive formula can also be obtained using the explicit formula as follows: Using the example above, we can write the explicit formula as follows: The explicit formula for an arithmetic sequence is given as: However, it is also possible to represent this same pattern using an explicit formula that directly calculates the nth term of the sequence. ![]() Thus, the employee will earn $2200 after five months of employment. To find the salary for the fifth month, we can use the recursive formula to find a_5 as follows: Starting from the initial salary of $2000, we can write recursive formula as follows: To calculate this, we can model the salary pattern as an arithmetic sequence with a common difference of $50. For instance, assume that an employer wants to determine how much an employee will earn after five months of employment if their salary is $2000 initially and is expected to increase by $50 every month. It is vital to know how to write these formulas in a real-world context because it can help solve practical problems and make accurate predictions about future outcomes.Īrithmetic sequences are patterns where each term is obtained by adding a constant value, known as the common difference (d), to the previous term. These sequences are often modeled using recursive and explicit formulas that give a straightforward representation of the patterns that govern them. ![]() ![]() Arithmetic and geometric sequences are an essential aspect of math, and they are widely used in the real-world setting. ![]()
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