Final answer:
To graph the sequence an=4n+3 on a graphing calculator, input the formula into the sequence mode, set n from 1 to 10, and use the 'Graph' function to view the linear pattern of the first 10 terms.
Step-by-step explanation:
To graph the first 10 terms of the sequence an=4n+3 using a graphing calculator, you can follow these steps:
- Turn on your graphing calculator (such as a TI-83 or TI-84).
- Enter the sequence function by pressing the 'seq' button or accessing the sequence mode, depending on your calculator model.
- Input the formula for the nth term of the sequence, which is 4n+3 in this case.
- Set the variable n to vary from 1 to 10 since we are interested in the first 10 terms.
- After entering all necessary information, choose the 'Graph' function to visualize the sequence.
- The calculator will display the points representing the terms of the sequence, which should form a linear pattern due to the arithmetic nature of the given sequence.
- Optionally, you can create a table of values to see the exact terms of the sequence by choosing the 'Table' function.
If you have the option, you can also fit these data points with a linear equation using the calculator's regression function. The linear equation should have the form y=mx+b where m is the slope and b is the y-intercept, rounded to four decimal places.
Keep in mind that the specific keys and functions might vary depending on the calculator model you are using. Be sure to refer to your calculator's manual for the precise sequence of steps.