Texas Instruments TI-92 Getting Started page 31

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Graphing Technology Guide: TI-92
Figure 5.84: Iteration
Press ENTER several more times and see what happens with this iteration. You may wish to try it again with a
different starting value.
5.7.2 Arithmetic and Geometric Sequences: Use iteration with the ANS variable to determine the n-th term of a
sequence. For example, find the 18th term of an arithmetic sequence whose first term is 7 and whose common
difference is 4. Enter the first term 7, then start the progression with the recursion formula, 2nd ANS + 4 ENTER.
This yields the 2nd term, so press ENTER sixteen more times to find the 18th term. For a geometric sequence
whose common ratio is 4, start the progression with 2nd ANS x 4 ENTER.
Figure 5.85: Sequential Y= menu Figure 5.86: Sequence mode
You can also define the sequence recursively with the TI-92 by selecting Sequence in the Graph type on the first
page of the MODE menu (see Figure 5.1). Once again, let's find the 18th term of an arithmetic sequence whose first
term is 7 and whose common difference is 4. Press MODE 4[Sequence] ENTER. Then press Y= to edit any
of the TI-92's sequences, u1 through u99. Make u1(n) = u1(n – 1) + 4 and u1(1) = 7 by pressing U 1 ( N – 1) + 4
ENTER 7 ENTER (Figure 5.85). Press 2nd QUIT to return to the Home screen. To find the 18th term of this
sequence, calculate u1(18) by pressing U 1 ( 18 ) ENTER (Figure 5.86).
Of course, you could also use the explicit formula for the n-th term of an arithmetic sequence t = a + (n –1)d . First
n
enter values for the variables a, d, and n, then evaluate the formula by pressing A + ( N – 1 ) D ENTER. For a
n–1
geometric sequence whose n-th term is given by t = a · r , enter values for the variables a, d, and r, then evaluate
n
the formula by pressing A R ∧ ( N – 1) ENTER.
To use the explicit formula in Seq MODE, make u (n) = 7 + (n –1) · 4 by pressing Y= then using to move up
1
to the u1(n) line and pressing CLEAR 7 + ( N – 1) × 4 ENTER 2nd QUIT. Once more, calculate u1(18) by
pressing U 1 ( 1 8) ENTER.
5.7.3 Finding Sums of Sequences: You can find the sum of a sequence by combining the features sum( and seq(
feature on the LIST sub-menu of the MATH menu. The format of the sum( command is sum(list). The format of
the seq( command is seq(expression, variable, low, high, step) where the step argument is optional and the
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∑
n
default is for integer values from low to high. For example, suppose you want to find the sum 4(0.3) . Press 2nd
n= 1
MATH 3[LIST] 6[sum(] 2nd MATH 3[LIST] 1[seq(] 4 ( . 3 ) ∧ K , K , 1, 12 ) ) ENTER (Figure 5.87). The seq(
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