Here we answer many questions about the sequence 21, 84, 336, 1344... What type of sequence is 21, 84, 336, 1344? What is the next number in the sequence 21, 84, 336, 1344? What is the nth number in the sequence 21, 84, 336, 1344? What is the sum of the first 10 terms in the sequence 21, 84, 336, 1344? What is the sum of the first n numbers in the sequence 21, 84, 336, 1344?
In addition, we will also give you the formula that is used to calculate the next number or the nth number in 21, 84, 336, 1344, and the formula to calculate the sum of n numbers in 21, 84, 336, 1344.
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 21, 84, 336, 1344? The sequence 21, 84, 336, 1344 has a common ratio of 4 between each term. We call this kind of sequence a geometric sequence. Below is an image illustrating the correlation between the geometric sequence 21, 84, 336, 1344 and its common ratio of 4.
Now, what is the next number in the sequence 21, 84, 336, 1344? Below is the formula used to calculate the next number in a geometric sequence, such as 21, 84, 336, 1344. The first term listed in the sequence is "a", the common ratio is "r", and "n" is the nth term of the geometric sequence.
a × r^(n-1) = Next Term
As stated above, the common ratio (r) between each term is 4. Furthermore, the next term in 21, 84, 336, 1344 is the fifth term (5), and the first term is 21. When we enter these values into our formula, we get the following answer:
21 × 4^(5-1) = 5376
Thus, the next number (term) in the sequence 21, 84, 336, 1344 is 5376. 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 21, 84, 336, 1344, or 100 if you want the 100th term in the sequence 21, 84, 336, 1344.
Let's move on to our next question. What is the sum of the first 10 terms in the sequence 21, 84, 336, 1344? We use the formula below to calculate the sum of the first n terms in a geometric sequence such as 21, 84, 336, 1344. Again, note that the first term is "a", the common ratio is "r", and "n" is the nth term of the geometric sequence.
(a × (1 - r^n)) ÷ (1 - r) = Sum
When we enter the a, r, and n values into our formula, where n is equal to 10, we can calculate the sum of all numbers up through the 10th term in the sequence 21, 84, 336, 1344, as seen below:
(21 × (1 - 4^10)) ÷ (1 - 4) = 7340025
Therefore, the sum of all numbers up through the 10th term in the sequence 21, 84, 336, 1344 is 7340025. 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 21, 84, 336, 1344 using the formula mentioned above. For example, if you type in 15, then it will calculate the sum of the first 15 terms in the sequence 21, 84, 336, 1344.
Geometric Sequence Calculator
Go here to learn more about geometric sequences using the best online Geometric Sequence Calculator.
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