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Quadratic sequences are sequences that include an term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.
Un= an^2+ an + b
Example: 2, 5, 10, 17, 26
+3, +5, +7, +9
+2, +2, +2, +2
2/2 = 1
n^2
1^2 = 1
2^2= 4
3^2 =9
4^2 = 16
5^2= 25
2, 5, 10, 17, 26
-1, 4, 9, 16, 25
1, 1, 1, 1, 1
So, it will be
n^2+1

Another example: 3, 9, 17, 27, 39
+6, +8, +10, +12
+2, +2, +2, +2
2/2 = 1
n^2
3, 9, 17, 27, 39
-1, 4, 9, 16, 25
2, 5, 8, 11, 14
-3, 6, 9, 12, 15
n^2+3n-1

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Finished soon!! wait for the explanation✨✨

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Finished soon!! wait for the explanation✨✨

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So, there are some real life situation of sequence that is needed .

Sequences are useful in our daily lives as well as in higher mathematics. For example, the interest portion of monthly payments made to pay off an automobile or home loan, and the list of maximum daily temperatures in one area for a month are sequences.

Aplication of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. Fibonacci appears in biological settings such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts. Sunflower seed is using golden ratio or fibonaci sequence to provide more space to grow.

One real life situation that Pascal's triangle is used for is probability and combinations. We have situations like this all of the time. For example, say you are at an ice cream shop and they have 5 different ice creams. You want to know how many different ways you can pick two of the ice creams and eat them. In 1653, a French mathematician-philosopher named Blaise Pascal described a triangular arrangement of numbers corresponding to the probabilities involved in flipping coins, or the number of ways to choose 'n' objects from a group of 'm' indistinguishable objects. Pascal's triangle has many uses in binomial expansions. Every row is built from the row above it. Pascal's triangle gives us the coefficients for an expanded binomal of the form (a + b)n, where n is the row of the triangle. The Binomal Triangle tells us we can use these coefficients to find the entire expanded binomal, with a couple extra tricks thrown in.

Quadratic sequence are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. A real world example of a cubic function might be the change in volume of a cube or sphere, depending on the change in the dimensions of a side or radius, respectively.

There are many uses of geometric sequence in everyday life, but one of the most common is in calculating interest earned. Mathematicians calculate a term in the series by multiplying the initial value in the sequence by the rate raised to the power of one less than the term number. They have important applications in physics, engineering, biology, economics, computer science, queueing theory, and finance. Geometric series are one of the simplest examples of infinite series with finite sums, although not all of them have this property.

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In a Geometric sequence each term is found by multiplying the previous term by a constant.

Example :
1, 2, 4, 8, 16, 32, 64, 128, 256, ...

This sequence has a factor of 2 between each number.

Each term (except the first term) is found by multiplying the previous term by 2.

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Cubic sequences are characterized by the fact that the third difference between its terms is constant.
Un= an^3 + an^2 +an + b
For example, consider the sequence:

4,14,40,88,164,…4,14,40,88,164,…

looking at the first, second and third difference of this sequence would look like:

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A number pattern which increases or decrease by the same amount each time is called a linear sequence. The amount it increases or decreases by is known as the common difference.
Example:
6, 11, 16, 21, 26...
1) What is the n term? 5n+1
2) 13th: 5(13)+1 = 66
3) Is 71 a term in the sequence?
71-1=70
5n = 70
5n÷5 = 70÷5
n = 14
Yes, it is the 14th term in the sequence.

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Pascal's triangle begins at the top with the number 1. The following line starts and ends with the number 1. Other numbers in a line are obtained by summing up the two numbers in the line before.

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Identifying even and odd numbers is an important skill that children need to help them understand our number system and aid in their preparation to group whole number operations. It will also help prepare them to learn division, prime numbers and even square roots. An odd number is not divisible evenly by two.

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An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.

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An arithmetic sequence is a series of numbers obtained by adding (or subtracting) the same value with each step. A child’s counting sequence (1, 2, 3, 4, . . .) is a simple arithmetic sequence, where the common difference is 1: that is, each adjacent number in the sequence differs by a value of one.

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A particular order in which related things follow each other.

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Why sequence is important in our daily life?

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Why sequence is important in our daily life?

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there was an order and sequence that should be followed in the morning. Sequence and order in everyday life routines provides stability for our children, but it also helps them think about other moments when sequencing might be important.

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Sequence of even number:
-2,4,6,8
Sequence of odd number:
-1,3,5,7
The arrangement of pattern is also known as 'sequence' which can be determined by comparing consecutive pattern:
- 16,18,20,22
The pattern of a sequence can be indentified by finding the relation between the numbers in that sequence
-1,7,13,19

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The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it:

the 2 is found by adding the two numbers before it (1+1),
the 3 is found by adding the two numbers before it (1+2),
the 5 is (2+3),
and so on!

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Here is a longer list:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...

Can you figure out the next number?