Which of the following Is an Arithmetic Sequence?

An arithmetic sequence is a sequence of numbers in which each number is the previous number plus a constant. The constant is called the common difference. For example, the sequence 5, 10, 15, 20, 25 is an arithmetic sequence because each number is 5 more than the previous number. The common difference is 5.

An arithmetic sequence can be represented by the equation an = a1 + (n - 1)d, where a1 is the first term in the sequence, n is the number of the term, and d is the common difference.

There are many types of sequences that are not arithmetic sequences. For example, the sequence 2, 4, 6, 8, 10 is not an arithmetic sequence because the common difference is not a constant. The common difference between the first two terms is 2, but the common difference between the second and third terms is only 4 - 2 = 2. So, this sequence is not an arithmetic sequence.

The sequence 1, 2, 4, 8, 16 is also not an arithmetic sequence. In this sequence, each term is double the previous term. This sequence is called a geometric sequence.

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An arithmetic sequence is a mathematical concept that deals with the order and relationships of numbers. The name comes from the Greek words for "order" and "number". In an arithmetic sequence, each number after the first is called a "term" and is obtained by adding a certain value, called the "common difference", to the previous term. The general form of an arithmetic sequence is:

a, a+d, a+2d, a+3d, ...

where "a" is the first term in the sequence, "d" is the common difference, and the ellipsis indicates that the pattern continues.

The common difference can be positive or negative, but it cannot be zero, since that would mean that all terms in the sequence would be the same. For example, the sequence 3, 5, 7, 9, ... has a common difference of 2, while the sequence 9, 6, 3, 0, ... has a common difference of -3.

The common difference can be thought of as the slope of the line connecting any two consecutive terms in the sequence. In the first example above, the slope is 2; in the second example, the slope is -3. In general, the slope of an arithmetic sequence is the common difference.

The common difference can also be thought of as the amount by which each term in the sequence differs from the previous term. In the first example above, each term differs from the previous term by 2; in the second example, each term differs from the previous term by -3. In general, the difference between any two consecutive terms in an arithmetic sequence is the common difference.

The terms of an arithmetic sequence are equally spaced; that is, the difference between any two consecutive terms is the same. This is why the common difference is also sometimes called the "constant difference".

The common difference can be found by subtracting the first term from the second term, the second term from the third term, and so on. In the first example above, the common difference is 2 because 5-3=2, 7-5=2, and 9-7=2. In the second example, the common difference is -3 because 6-9=-3, 3-6=-3, and 0-3=-3.

It is also possible to find the common difference by subtracting the last term from the first term and then dividing

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In an arithmetic sequence, each term after the first is obtained by adding the common difference to the preceding term. The common difference is the number that is added (or subtracted) to each term to generate the next term in the sequence. For example, the common difference between consecutive terms in the sequence 4, 7, 10, 13, 16, 19, 22 is 3.

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An arithmetic sequence is a list of numbers in which each number is the same amount more than the one before it. The common difference between successive terms of an arithmetic sequence is denoted by d.

The nth term of an arithmetic sequence is given by the formula:

nth term = a + (n - 1)d

where "a" is the first term in the sequence and "d" is the common difference between successive terms.

Therefore, to find the nth term of an arithmetic sequence, one must first determine the value of "a" and "d". Once these values are known, the nth term can be calculated using the formula above.

For example, consider the arithmetic sequence: 3, 5, 7, 9, 11, 13, 15...

In this sequence, "a" equals 3 and "d" equals 2. Therefore, the nth term would be calculated as:

nth term = 3 + (n - 1)2

For n = 3, the term would be 3 + (3 - 1)2 = 3 + 2 = 5.

Similarly, for n = 5, the term would be 3 + (5 - 1)2 = 3 + 8 = 11.

In general, the nth term of an arithmetic sequence can be found by using the formula above.

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In mathematics, an arithmetic sequence, also known as an arithmetic progression, is a sequence of numbers such that the difference between any two consecutive terms is a constant. For instance, the sequence 5, 7, 9, 11, 13, 15, 17, 19, . . . is an arithmetic sequence with common difference of 2. An arithmetic sequence with a common difference of 1 is called a linear sequence.

The sum of the first n terms of an arithmetic sequence is given by the formula:

S= n/2 * (a1 + an)

Where a1 is the first term of the sequence and an is the nth term of the sequence.

For example, let's find the sum of the first 10 terms of the arithmetic sequence whose first term is 2 and common difference is 3. We can use the formula above:

S= 10/2 * (2 + 2+3+3+4+4+5+5+6+6) S= 10/2 * (2 + 29) S= 10/2 * 31 S= 155

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An arithmetic sequence is a sequence where each term is the previous term plus a constant. A geometric sequence is a sequence where each term is the previous term multiplied by a constant.

There are many properties that can be associated with an arithmetic sequence. To begin with, an arithmetic sequence is a sequence of numbers in which each number is the previous number plus a fixed number. So, for example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence because each number is two more than the previous number. The fixed number in this instance is called the common difference.

Another property that can be associated with an arithmetic sequence is that the difference between any two consecutive numbers in the sequence is always the same. So, using the example above, the difference between 2 and 5 is 3, the difference between 5 and 8 is 3, the difference between 8 and 11 is 3, and the difference between 11 and 14 is also 3. This property can be used to easily calculate any number in the sequence if the first number and the common difference are known.

Arithmetic sequences also have what is known as a recursive property. This means that the nth number in the sequence can be found by adding the common difference to the (n-1)th number. So, using the example above, the 5th number in the sequence would be 14 (11+3).

Finally, it can be said that all arithmetic sequences have a definite pattern. This pattern becomes apparent when the numbers in the sequence are graphed. When graphed, all arithmetic sequences will appear as a straight line.

Overall, there are many properties that can be associated with an arithmetic sequence. These properties include the common difference, the recursive property, and the fact that all arithmetic sequences have a definite pattern. These properties can be used to help calculate numbers in a sequence and to better understand the patterns that exist within arithmetic sequences.

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In mathematics, an arithmetic sequence, also known as an arithmetic progression, is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, ... is an arithmetic sequence with common difference 2. An arithmetic sequence generally has the form:

a, a+d, a+2d, a+3d, ...

where d is the common difference.

The nth term of an arithmetic sequence is denoted by un or un−1, depending on the convention used. For example, u5 would refer to the fifth term of the sequence.

Arithmetic sequences are often generated by adding a constant to the previous term; that is, they have the form:

un = un−1 + d.

Geometric sequences have a similar form, except that each term is multiplied by a common ratio r:

un = un−1 × r.

The sum of the first n terms of an arithmetic sequence is called an arithmetic series. For example, the sum of the first 10 terms of the sequence 2, 4, 6, 8, 10, 12, ... is

2 + 4 + 6 + 8 + 10 + 12 + ... + 20 = 110.

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An arithmetic sequence is a sequence where each term after the first is obtained by adding a fixed number, called the common difference, to the previous term. The sum of an arithmetic sequence is the total of all the terms in the sequence. The formula for the sum of an arithmetic sequence is:

S = n/2 * (a1 + a2)

where n is the number of terms in the sequence, and a1 and a2 are the first and last terms in the sequence.

In mathematics, an arithmetic sequence is a sequence of numbers such that the difference between any two successive members is a constant. For instance, the sequence 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,... is an arithmetic sequence with a common difference of 2.

The nth term of an arithmetic sequence is given by the formula:

nth term = first term + (n - 1) x common difference

where "first term" is the first term in the sequence, "n" is the position of the term in the sequence, and "common difference" is the common difference between successive terms in the sequence.

For example, in the arithmetic sequence 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,...

The first term is 5

The second term is 7

The third term is 9

The fourth term is 11

The fifth term is 13

and so on...

Therefore, the 10th term in this sequence is 5 + (10 - 1) x 2 = 5 + 9 x 2 = 5 + 18 = 23