Final answer:
To find the common difference of an arithmetic sequence, subtract a term from the following one in the sequence; this difference is constant. Using a calculator like the TI-83+ or TI-84 can automate this by calculating the differences between corresponding entries in two lists. This concept also applies to broader change calculations with 'final value minus initial value'.
Step-by-step explanation:
To find the common difference of an arithmetic sequence, take any two consecutive terms and subtract the earlier term from the later term. This difference is constant throughout the entire sequence. For example, if our sequence is 3, 7, 11, 15, and so on, the common difference is calculated by subtracting the first term from the second term: 7 - 3 = 4, which is our common difference.
You can also use a calculator to find the common difference. On a TI-83+ or TI-84, you can enter your sequence values into two separate lists. If you put the 'after' values in the first list and the 'before' values in the second list, you can create a third list that calculates the difference for each pair of terms. To do this, arrow up to the name of the third list and enter the formula 1st list name - 2nd list name. The calculator will perform the subtraction, and the third list will display the resulting differences, confirming the common difference if you have an arithmetic sequence.
If you want to determine the change in broader contexts, such as in data analysis or calculating change in variables, remember to use the 'final value minus initial value' approach. This can help deduce changes in trends over time or calculate interest by finding the difference between the future value and the present value.