Geometric sequences and series
Enter a sequence Enter a sequence (recursive definition) Graph a sequence Calculate a term of a sequence Graph a series Calculate the value of a series

Enter a sequence on your calculator

Suppose you want to enter the sequence \(u_n = u_1 \cdot \left(\frac{1}{2}\right)^n\) with \(u_1 = 0.3\) on your calculator.

  1. Create a new document, press Menu Icon and select Add Calculator.
  2. Press Menu Icon, select Actions > Define.
  3. Type u(n), then write the expression of the sequence.

    Sequence Expression Screen

Enter a sequence on your calculator (recursive definition)

Suppose you want to enter the sequence \(u_n = \frac{1}{2} \cdot u_{n-1}\), with \(u_1 = 0.3\) on your calculator.

  1. Create a new document, press Menu Icon and select Add Calculator.
  2. Press Menu Icon, select Actions > Define.
  3. Type u(n), press Enter Icon and select.
  4. On the first line, write the initialization. On the second line, write the recursive expression.

    Recursive Sequence Screen

Graph a sequence

Suppose you want to display the graph of the sequence \(u_n = u_1 \cdot \left(\frac{1}{2}\right)^n\) with \(u_1 = 0.3\) on your calculator, starting at \(n = 1\) and ending at \(n = 20\).

  1. Create a new document, press Menu Icon and select Add Graphs.
  2. Press Menu Icon, select Graph Entry/Edit > Sequence > Sequence.
  3. In the first line, write the expression of the sequence. In the second line, write the number of initial terms.

    Graph Expression Screen

  4. Press Enter Icon and the graph of the sequence is displayed.

    Graph Result Screen

Compute a term of a sequence

Suppose you want to know the 320th term of the sequence \(u_n = u_1 \cdot \left(\frac{1}{2}\right)^n\) with \(u_1 = 0.3\).

  1. Enter the sequence on your calculator (see instructions above).
  2. Press Enter Icon and write u(320) in the following line.

    Term Calculation Screen

Graph a series

Suppose you want to graph the series of the sequence \(u_n = u_1 \cdot \left(\frac{1}{2}\right)^n\) with \(u_1 = 0.3\) on your calculator, starting at \(n = 1\) and ending at \(n = 20\).

  1. Enter the sequence on your calculator (see instructions above).
  2. Enter the series of the sequence in the line below. To do this, define s(n) =.

    Series Step 2 Screen

  3. Create a new document, press Menu Icon and select Add Graphs.

    Series Step 3 Screen

  4. Press Menu Icon, select Graph Entry/Edit > Sequence > Sequence.
  5. In the first line, write s(n). In the second line, write the number of initial terms.
  6. Press Enter Icon and the graph of the series is displayed.

    Series Result Screen

Compute the value of a series

  1. Enter the sequence on your calculator (see instructions above).
  2. Enter the series of the sequence in the line below.
  3. Type s(20) to set the ending of the series at \(n = 20\). Press Enter Icon. The result should be \(0.3\).

    Series Value Result Screen