Answer:
The following observation and calculations show that the iterative rule is correct.
Step-by-step explanation:
The second reason why these calculations are true is the fact these calculations represent geometric sequence.
Considering the data
200, 220, 242, 266.2, 292.82, 322.102,....
Any sequence is said to be the geometric sequence If the ratio between two consecutive terms remains constant - commonly known as common ration which is denoted by 'r'.
As the ratio between two consecutive terms remains constant. For example,
[tex]r=\frac{220}{200} =1.1, r=\frac{242}{220} =1.1, r=\frac{266.2}{242} =1.1[/tex]
So, the given sequence is a geometric sequence. In other words, in Geometric Sequence each term can be found in terms of multiplying the previous term by a constant factor which is 1.1.
So,
220 is obtained by multiplying 200 by 1.1.
i.e. 200×1.1 = 220
Also,
242 is obtained by multiplying 220 by 1.1.
i.e. 220×1.1 = 242
and so on...
Therefore, it is clear from the current observation and calculation that the iterative rule is correct.
Keywords: sequence, geometric sequence
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