Here we answer many questions about the sequence 2, 6, 10, 14... What type of sequence is 2, 6, 10, 14? What is the next number in the sequence 2, 6, 10, 14? What is the nth number in the sequence 2, 6, 10, 14? What is the sum of the first 20 terms in the sequence 2, 6, 10, 14? What is the sum of the first n numbers in the sequence 2, 6, 10, 14?
In addition, we will also give you the formula that is used to calculate the next number or the nth number in 2, 6, 10, 14, and the formula to calculate the sum of n numbers in 2, 6, 10, 14.
A sequence is a list of numbers in a pattern, and each number in the sequence is called a term. We will use "terms" and "numbers" interchangeably on this page.
So, what type of sequence is 2, 6, 10, 14? The sequence 2, 6, 10, 14 has a common difference of +4 between each term. We call this kind of sequence an arithmetic sequence. Below is an image illustrating the correlation between the arithmetic sequence 2, 6, 10, 14 and its common difference of +4.
Now, what is the next number in the sequence 2, 6, 10, 14? Below is the formula used to calculate the next number in an arithmetic sequence, such as 2, 6, 10, 14. The first term listed in the sequence is "a", the common difference is "d", and "n" is the nth term of the arithmetic sequence.
a + (n-1) × d = Next Term
As stated above, the common difference (d) between each term is +4. Furthermore, the next term in 2, 6, 10, 14 is the fifth term (5), and the first term is 2. When we enter these values into our formula, we get the following answer:
2 + (5 - 1) × 4 = 18
Thus, the next number (term) in the sequence 2, 6, 10, 14 is 18. The tool below calculates the nth term of the sequence using the formula above. For example, type in 20 if you want the 20th term in the sequence 2, 6, 10, 14, or 100 if you want the 100th term in the sequence 2, 6, 10, 14.
Let's move on to our next question. What is the sum of the first 20 terms in the sequence 2, 6, 10, 14? We use the formula below to calculate the sum of the first n terms in an arithmetic sequence such as 2, 6, 10, 14. Again, note that the first term is "a", the common difference is "d", and "n" is the nth term of the arithmetic sequence.
(n/2)((2 × a) + (n - 1) × d) = Sum
When we enter the a, d, and n values into our formula, where n is equal to 20, we can calculate the sum of all numbers up through the 20th term in the sequence 2, 6, 10, 14, as seen below:
(20/2)((2 × 2) + (20 - 1) × 4) = 800
Therefore, the sum of all numbers up through the 20th term in the sequence 2, 6, 10, 14 is 800. Below is another tool we created to make these calculations easier for you. This tool can calculate the sum of any number of terms in the sequence 2, 6, 10, 14 using the formula mentioned above. For example, if you type in 50, then it will calculate the sum of the first 50 terms in the sequence 2, 6, 10, 14.
Arithmetic Sequence Calculator
Go here to learn more about arithmetic sequences using the best online Arithmetic Sequence Calculator.
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