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

Lapatulllka [165]

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,

a. 12, 144, 1728,..

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.

b. 0,5, 10, 15, 20, 25,...

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

c. 0,4, 16, 36, 64,...

Here

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

Common Difference:

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

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

d. 1.5, 2.25, 3.375, 5.0625,...

Here

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

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

Keywords: Sequence, Ratio

Learn more about sequences at:

#LearnwithBrainly

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Consider the quadratic function f(y) = 8y2 – 7y + 6. What is the constant of the function?

Over [174]

The constant is 6. A constant is just the number on its own. Quadratics follow the form f(x) = ax^2+bx+c. The c is the constant.

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3 years ago

How can you tell if a number is divided by 4

Elan Coil [88]

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Do rational expressions contain logarithmic functions? A. always B. sometimes C. never

bazaltina [42]

The right answer is C. never

The quotient of two algebraic expressions is a fractional expression. Moreover, the quotient of two polynomials such as:

$\frac{1}{x} \\ \\ \frac{3x-2}{1+x} \\ \\ \frac{x^2-4}{x^2+2}$

is called a rational expression. So according to this definition rational expressions does not contain logarithmic functions. In fact, a rational expression is an expression that is the ratio of two polynomials like this:

$f(x)=\frac{P(x)}{Q(x)} \\ \\ with \ Q(x) \neq 0$