What is the nth term rule of the linear sequence below 5 7 9 11 13?

The nth term rule of a linear sequence refers to the formula or equation that can be used to find any term in the sequence, based on its position or index. In this case, we have a linear sequence with the terms 5, 7, 9, 11, 13.

To find the nth term rule for this sequence, we need to identify any patterns or relationships between the terms. Let's examine the differences between consecutive terms:

• The difference between 7 and 5 is 2
• The difference between 9 and 7 is 2
• The difference between 11 and 9 is 2
• The difference between 13 and 11 is 2

As we can see, the differences between consecutive terms are all 2. This indicates that each term in the sequence is obtained by adding 2 to the previous term. Therefore, the nth term rule of this linear sequence is:

nth term = 2n + 3

This means that to find the nth term in the sequence, we multiply the position (n) by 2 and add 3 to the result. For example, if we want to find the 10th term, we would substitute n = 10 into the equation:

10th term = 2(10) + 3 = 23

So the 10th term of this sequence would be 23.

What is the nth term rule of 5 7 9 11?

The nth term rule is a mathematical formula that allows us to find the value of any term in a sequence. In this case, we are given the sequence 5, 7, 9, 11, and we want to find a rule to determine the value of any term in the sequence.

The first step in finding the nth term rule is to observe the pattern in the sequence. In this case, we can see that each term is obtained by adding 2 to the previous term. This means that each subsequent term is 2 more than the previous term.

Now, we can write the nth term rule for this sequence. Let's assume that the first term is represented by 'a' and the common difference between terms is 'd'. The nth term rule can be written as: a + (n-1) * d. In our sequence, the first term is 5 and the common difference is 2, so the nth term rule for this sequence is: 5 + (n-1) * 2.

For example, if we want to find the value of the 6th term in this sequence, we can substitute n = 6 into the nth term rule: 5 + (6-1) * 2 = 5 + 5 * 2 = 5 + 10 = 15. Therefore, the 6th term in the sequence is 15.

In conclusion, the nth term rule of the sequence 5, 7, 9, 11 is 5 + (n-1) * 2, where n represents the position of the term in the sequence. This rule allows us to find the value of any term in the sequence by substituting the position of the term into the formula.

What is the nth term or nth rule of the sequence 1 5 9 13?

The sequence 1, 5, 9, 13 is an arithmetic sequence. In an arithmetic sequence, each term is found by adding a constant value, called the common difference, to the previous term. To find the nth term or nth rule of this sequence, we need to determine the common difference.

We can find the common difference by subtracting any two consecutive terms in the sequence. Let's subtract the first term (1) from the second term (5):

5 - 1 = 4

Therefore, the common difference of this sequence is 4.

Now that we know the common difference, we can determine the nth term or nth rule of the sequence. The nth term of an arithmetic sequence can be found using the formula:

a_n = a₁ + (n - 1)d

Where a_n represents the nth term, a₁ represents the first term, n represents the position of the term in the sequence, and d represents the common difference.

Let's use this formula to find the nth term of the sequence 1, 5, 9, 13:

a_n = 1 + (n - 1)4

Simplifying the equation gives us:

a_n = 1 + 4n - 4

a_n = 4n - 3

Therefore, the nth term or nth rule of the sequence 1, 5, 9, 13 is given by the formula a_n = 4n - 3. This formula allows us to find any term in the sequence by substituting the value of n into the equation.

What is the nth term rule of 7 9 11 13 15?

The sequence 7, 9, 11, 13, 15 follows a specific pattern known as the nth term rule. This rule helps us determine the value of any term in the sequence based on its position or index.

The nth term rule of this sequence is identified by the formula:

n + 6

Here, n represents the position of a term in the sequence, starting from 1.

Let's understand this rule by calculating the value of a few terms in the sequence:

The first term (n = 1): 1 + 6 = 7

The first term of the sequence is 7, which corresponds to n = 1 when we plug it into the formula. This validates that the nth term rule correctly identifies the value of the first term.

The second term (n = 2): 2 + 6 = 9

Similarly, when we substitute n = 2 into the formula, we get a value of 9. This matches the second term in the sequence.

The third term (n = 3): 3 + 6 = 11

Continuing with the same pattern, the third term of the sequence is found by substituting n = 3 into the formula. The result is 11.

The fourth term (n = 4): 4 + 6 = 13

Applying the nth term rule again, we determine that the fourth term in the sequence is 13.

The fifth term (n = 5): 5 + 6 = 15

Finally, when we substitute n = 5, we find that the fifth term of the sequence is indeed equal to 15, completing the pattern.

In conclusion, the nth term rule of the sequence 7, 9, 11, 13, 15 is represented by the formula n + 6. This formula allows us to determine the value of any term in the sequence by substituting its position or index into the formula.

What is the term to term rule of the linear sequence below 7 9 11 13 15?

In this linear sequence, each term increases by 2.

The term to term rule can be described as a constant increment of 2.

Starting from the first term, which is 7, we add 2 to get the next term, 9.

Similarly, we keep adding 2 to the previous term to find the subsequent terms. For example, we add 2 to 9 to get 11, and so on.

The rule is consistent throughout the sequence, where each term is obtained by adding 2 to the previous term.

Therefore, the term to term rule for the given linear sequence is to add 2 to each term to obtain the next term in the sequence.