Casio FXCP400 6-2Graphing a Recursion, About rSolve, About LinkTrace, Calculating the Sum of a Sequence, Determining the General Term of a Recursion Expression

Determining the General Term of a Recursion Expression

You can use the rSolve function to convert the sequence expressed by a recursion expression to the general term format an = f(n).

0602 To determine the general term of the recursion expression an+1 = an + 2, a1 = 1

About rSolve

The rSolve function returns the explicit formula of a sequence that is defined in relation to one or two previous terms, or a system of recursive formulas.

Syntax: rSolve (Eq, initial condition-1[, initial condition-2] [ ) ]

rSolve ({Eq-1, Eq-2}, {initial condition-1, initial condition-2} [ ) ] (Eq: Equation)

Example: To obtain the n-th term of a recursion formula an+1 = 3an – 1 with the initial conditions a1 = 1

Calculating the Sum of a Sequence

Perform the following steps when you want to determine the sum of a specific range of the sequence of a recursion expression or a general term expression.

0603 To calculate the sum of the general term expression anE = n2 + 2n – 1 in the range of 2 s n s 10

6-2 Graphing a Recursion

ClassPad lets you graph the values in a number table you create, and draw a cobweb diagram from the recursion expression.

0604 To input the expression an+1 = 2an + 1, a1 = 1, create a number table, and graph the values in the table 0605 To input the expression an+1 =  ￿ − 1, a1 = 0.5 and draw a cobweb diagram

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About LinkTrace

While the Table and Graph windows are on the display, you can activate LinkTrace. To do this, tap in the Table window to make it active. Next, tap aand then [Link]. While LinkTrace is active, the pointer on the Graph window jumps automatically to the point indicated by the coordinates in the currently selected table cell. Note that LinkTrace does not work when the selected cell is in the first column (column n).

Chapter 6: Sequence Application 127