Hence,
a. 12, 144, 1728,.. => Geometric
b. 0,5, 10, 15, 20, 25,... => Arithmetic
c. 0,4, 16, 36, 64,... => Neither arithmetic nor geometric
d. 1.5, 2.25, 3.375, 5.0625,... => Geometric
Step-by-step explanation:
In order to identify the sequence as geometric or arithmetic sequence, we find the common difference and common ratio of the sequence. If the common difference is same, it is an arithmetic sequence and if the common ratio is same the sequence is a geometric sequence
Common difference is the difference between consecutive terms of an arithmetic sequence and common ration is the ratio between two consecutive terms of a sequence
So,
<u>a. 12, 144, 1728,..</u>
Here,
Common difference:
Common Ratio:
As the common ratio is same, the given sequence is a geometric sequence.
<u></u>
<u>b. 0,5, 10, 15, 20, 25,...</u>
Here,
Common difference:
As the common difference is same, the given sequence is an arithmetic sequence
<u></u>
<u>c. 0,4, 16, 36, 64,...</u>
Here
Common Difference:
<u></u>
Common Ratio:
Neither the common ratio nor common difference are same, so the given sequence is neither arithmetic nor geometric
<u>d. 1.5, 2.25, 3.375, 5.0625,...</u>
Here
<u></u>
Common Difference:
As the common ratio is same, given sequence is geometric
Hence,
a. 12, 144, 1728,.. => Geometric
b. 0,5, 10, 15, 20, 25,... => Arithmetic
c. 0,4, 16, 36, 64,... => Neither arithmetic nor geometric
d. 1.5, 2.25, 3.375, 5.0625,... => Geometric
<u>Keywords: Sequence, Ratio</u>
<u>Learn more about sequences at:</u>
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