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yKpoI14uk [10]
3 years ago
14

Identify the following sequences as arithmetic, geometric, or neither. For the arithmetic and geometric sequences, identify the

growth pattern.
a. 12, 144, 1728,..
b. 0,5, 10, 15, 20, 25,...
c. 0,4, 16, 36, 64,...
d. 1.5, 2.25, 3.375, 5.0625,...
Mathematics
1 answer:
Lapatulllka [165]3 years ago
4 0

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,

a_1=12\\a_2=144\\a_2=1728

Common difference:

d=a_2-a_1 = 144-12 = 132\\=a_3-a_2 = 1728-144=1584

Common Ratio:

r=\frac{a_2}{a_1} =\frac{144}{12} = 12\\=\frac{a_3}{a_2}=\frac{1728}{144} =12

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,

a_1 = 0\\a_2 =5\\a_3 =10

Common difference:

d=a_2-a_1 = 5-0 = 5\\d=a_3-a_2 = 10-5 = 5

As the common difference is same, the given sequence is an arithmetic sequence

<u></u>

<u>c. 0,4, 16, 36, 64,...</u>

Here

a_1 = 0\\a_2 =4\\a_3 = 16\\a_4 = 36

Common Difference:

d= a_2-a_1 = 4-0 = 4\\a_3-a_2 = 16-4 = 12

<u></u>

Common Ratio:

r=\frac{a_2}{a_1} = \frac{4}{0} = Doesn't\ exist

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

a_1 = 1.5\\a_2 = 2.25\\a_3 = 3.375

<u></u>

Common Difference:

d=a_2-a_1 = 2.25-1.5 = 0.75\\a_3-a_2 =3.375-2.25 = 1.125[/tex]Common Ratio: [tex]r=\frac{a_2}{a_1} = \frac{2.25}{1.5}=1.5\\=\frac{a_3}{a_2} =\frac{3.375}{2.25}=1.5

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>

  • brainly.com/question/3783529
  • brainly.com/question/3799248

#LearnwithBrainly

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