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In any arithmetic sequence, the first term (often denoted as \(a_1\)) is crucial. It sets the starting point for the entire sequence.
Identifying the first term is straightforward—it is simply the very first number in the given sequence.
Let's look at our example: The sequence provided is \(2.5, 3, 3.5, 4, \text{...}\).
The first term is \(2.5\).
So, we write: \(a_1 = 2.5\).
This value is important because every subsequent term builds on this initial value.

The common difference is another key feature of an arithmetic sequence. It tells you how much you add (or subtract) each time to get from one term to the next.
To find the common difference (denoted as \(d\)), follow these steps:
Take any term in the sequence and subtract the term that came before it.
For our example sequence, we can calculate it step-by-step:

• First, subtract the first term from the second term: \(3 - 2.5 = 0.5\).
• Next, verify this difference with the third and fourth terms: \(3.5 - 3 = 0.5\) and \(4 - 3.5 = 0.5\).

Thus, the common difference for this sequence is \(0.5\).
This value tells us that each term is \(0.5\) larger than the one before it.

Step-by-step solutions help break down problems into manageable parts, making them easier to understand. Let's walk through the example problem step by step:

Step 1: Identify the Sequence
First, recognize that the sequence \(2.5, 3, 3.5, 4, \text{...}\) is an arithmetic sequence. An arithmetic sequence consists of numbers with a constant difference between consecutive terms.

Step 2: Determine the First Term
Next, identify the first term, which is the initial value in the sequence. Here, the first term (\(a_1\)) is \(2.5\).

Step 3: Find the Common Difference
Finally, find the common difference (\(d\)) by subtracting the first term from the second term: \(d = 3 - 2.5 = 0.5\). Verify this by checking other pairs of consecutive terms: \(3.5 - 3 = 0.5\) and \(4 - 3.5 = 0.5\).
This step-by-step approach ensures that you understand how to find both the first term and the common difference in any arithmetic sequence.