Follow these steps to evaluate a sequence defined recursively using a graphing calculator: • On the home screen, key in the value for the initial term a 1 and press [ENTER]. • Enter the recursive formula by keying in all numerical values given in the formula, along with the key strokes [2ND]ASS for the previous term a n − 1 .. Press [ENTER]. • Continue pressing [ENTER] to calculate the values for each successive term. For the following exercises, use the steps above to find the indicated term or terms for the sequence. 57. Find the first terms of the sequence a 1 = 87 111 , a n = 4 3 a n − 1 + 12 37 . Use the > Frac feature to give fractional results.
Follow these steps to evaluate a sequence defined recursively using a graphing calculator: • On the home screen, key in the value for the initial term a 1 and press [ENTER]. • Enter the recursive formula by keying in all numerical values given in the formula, along with the key strokes [2ND]ASS for the previous term a n − 1 .. Press [ENTER]. • Continue pressing [ENTER] to calculate the values for each successive term. For the following exercises, use the steps above to find the indicated term or terms for the sequence. 57. Find the first terms of the sequence a 1 = 87 111 , a n = 4 3 a n − 1 + 12 37 . Use the > Frac feature to give fractional results.
Follow these steps to evaluate a sequence defined recursively using a graphing calculator: • On the home screen, key in the value for the initial term
a
1
and press [ENTER]. • Enter the recursive formula by keying in all numerical values given in the formula, along with the key strokes [2ND]ASS for the previous term
a
n
−
1
.. Press [ENTER]. • Continue pressing [ENTER] to calculate the values for each successive term. For the following exercises, use the steps above to find the indicated term or terms for the sequence.
57. Find the first terms of the sequence
a
1
=
87
111
,
a
n
=
4
3
a
n
−
1
+
12
37
. Use the > Frac feature to give fractional results.
Write down the first five terms of the following recursively defined: sequence.
a₁2; an+1 = -2an +7
것이
a. -10, 30, -90, 270, -810
b. -13, -16, -19, -22, -25
c. -10, -13, -16, -19, -22
d. -10, -7, -4, -1, 2
Think back to the magical candy machine at your neighborhood grocery store. Suppose that the first time a
quarter is put into the machine 1 Skittle comes out. The second time, 3 Skittles, the third time 9 Skittles,
the fourth time, 27 Skittles, etc.
a. Find both a recursive and closed formula for how many Skittles the nth customer gets.
Recursive formula: an =
Closed formula:
an =
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