Answer:
Step-by-step explanation:The explicit equation for the description of the sequence can be written as:
\[a_x = 513 \times (1 - 0.12)^x\]
where \(a_x\) represents the term at position \(x\) in the sequence.
To understand the equation, let's break it down step by step:
1. The first term of the sequence is given as 513.
2. The sequence is decreasing by 12% with each term.
3. To express the decrease, we multiply the previous term by (1 - 0.12), which is the decimal form of the percentage decrease.
4. The exponent \(x\) represents the position of the term in the sequence. For example, when \(x = 1\), it represents the first term, when \(x = 2\), it represents the second term, and so on.
Let's take an example to illustrate this equation. If we want to find the 3rd term in the sequence, we substitute \(x = 3\) into the equation:
\[a_3 = 513 \times (1 - 0.12)^3\]
Simplifying this calculation, we have:
\[a_3 = 513 \times (0.88)^3\]
Calculating further, we find:
\[a_3 = 513 \times 0.681472\]
So, the 3rd term in the sequence is approximately 349.85.