HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 99
The Sequence Aplet, Recursive or non-recursive, First, second & general terms
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14 THE SEQUENCE APLET This aplet is used to deal with sequences, and indirectly series, in both non-recursive form (where Tn is a function of n) and implicit/recursive/iterative form (where Tn is a function of Tn-1 ). Recursive or non-recursive Examples of these types of sequences are: (explicit/non-recursive) T = 3n − 1 ..... {2,5,8,11,14,.....} n T = n2 n ..... {1, 4,9,16, 25,.....} T = 2n n ..... {2, 4,8,16,32,.....} (implicit/recursive) T n = 2Tn−1 −1 ;T = 2 1 T n = 5 − Tn−1 ;T = 2 1 T n = Tn−1 + Tn−2 ;T 1 = 1,T 2 =1 ..... {2,3,5,9,17 2,3, 2,3, 2 1,1, 2,3,5,8.....} As with most aplets, the Sequence aplet starts in the SYMB view when you enter formulas. The Sequence aplet uses the terminology U(N) rather than the other commonly used Tn for its definitions in order to avoid having to use subscripts which would not show up well on the screen. All functions of this type are assumed to be defined for the positive integers only - ie. for N = 1,2,3,4... First, second & general terms Each definition has three entries - U1(1), U1(2) and U1(N) (see above) but it is not always necessary to supply all three. For example, if the sequence is non-recursive then only the U1(N) entry needs to be filled in, with the other two entries calculated automatically from the definition as shown in the sequence of two screens shown right. 99
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