Question

How do you use a graphing calculator to graph the first 10 terms of the sequence given ${{a}_{n}}=10{{\left( 1.2 \right)}^{n-1}}?$

Answer 1

Hint: This type of question requires the use of a graphing calculator. Using any of the graphic calculators for example, Texas Instruments TI-84, or TI-83, we can plot the given sequence.

Complete step-by-step answer:
First, we need to turn on the calculator and set it up in the sequence mode. To set it in this sequence mode, we first click on MODE and use the arrow keys to navigate down to FUNC and then use the right arrow key to move right towards the SEQ key. We then need to press ENTER.
Once we have clicked enter, the calculator has entered the SEQ mode. We now need to exit from this MODE screen and to do that, we click the 2ND button first followed by the MODE button. The purpose of clicking the 2ND button is that the function written on the top of the keys becomes active- in this case it is the QUIT function that is activated.
Next, we press the 2ND button again and then the STAT key, which means we are eventually activating the LIST function, we get a list of headings such as NAMES, OPS and MATH. We use the right arrow key to navigate to OPS and we need to select option 5 which says $seq\left( {} \right.$ . To do this we just need to press the number 5 on the keypad. It automatically come back to the home screen displaying a function like $seq\left( {} \right..$
Next, we need to type in the formula given in the question inside the $seq\left( {} \right.$ function. We type in the buttons necessary to form the function and to add the n variable, we need to press a button that says X, T, O, n. Doing all this, we arrive at
$\Rightarrow seq\left( 10{{\left( 1.2 \right)}^{n-1}} \right.$
Now we press the ‘,’ - comma button followed by the variable that we are varying that is n.
$\Rightarrow seq\left( 10{{\left( 1.2 \right)}^{n-1}} \right.,n$
Next, we need to specify the starting point for the sequence which is 1, so we again press comma followed by 1.
$\Rightarrow seq\left( 10{{\left( 1.2 \right)}^{n-1}} \right.,n,1$
Next, we need to specify the ending point for the sequence which is 10, so we again press comma followed by 10 and finally close the function using the closing parenthesis.
$\Rightarrow seq\left( 10{{\left( 1.2 \right)}^{n-1}},n,1,10 \right)$
Now we need to press enter and the calculator shows the terms in sequence. To see more terms that are not visible, we use the right arrow to move right to see.
To turn this decimal list into fractions, we press the MATH key and enter the key twice. Now the terms will be displayed in fraction form.
To plot this, we need to press the key that says ‘y=’ and we see three rows.
In the first row, we give our input function and it looks like this,
$\Rightarrow \ddots u\left( n \right)=10{{\left( 1.2 \right)}^{n-1}}$
We then press the GRAPH button. And we get a graph of these points starting from 1. To alter the view of the points or scale of the graph, we press the WINDOW key and then change Xmin, Xmax, Ymin and Ymax accordingly. Then we again need to press WINDOW to get the plot. If we now press the TRACE button, it will show the coordinates of each point. X coordinate represents the value of n and Y coordinate represents the value of the function there.
Hence we have seen how to graph the given sequence ${{a}_{n}}=10{{\left( 1.2 \right)}^{n-1}}$ on a graphing calculator.

Note: To solve this question, the students need to have a good grip on how to use the graphing calculator and must know the basics of it. It will be much easier for the student to solve such problems then. Students are suggested to vary the values of the terms Xmin, Xmax, Ymin and Ymax in order to change the scale of the graph and learn a little more about the calculator.