6-3-5

Recursive and Explicit Form of a Sequence

Determining the General Term of a Recursion Expression

The following procedure converts the sequence expressed by a recursion expression to the general term format an = f (n).

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

uClassPad Operation

(1)Start up the Sequence Editor.

•If you have another application running, tap mand then H.

•If you have the Sequence application running, tap Oand then [Sequence Editor].

(2)Tap (or press) O, [Sequence RUN], [Calc], [rSolve], [n,an], [an+1], =, [n,an], [an], +, 2, ,, [a0,a1], [a1], =, 1, and then ).

(3)Press E.

uAbout 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

Example: To obtain the n-th term of a recursion formula an+2 – 4an+1 + 4an = 0 with the initial conditions a1 =1, a2 = 3

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