Here we answer many questions about the sequence 1, 6, 36, 216... What type of sequence is 1, 6, 36, 216? What is the next number in the sequence 1, 6, 36, 216? What is the nth number in the sequence 1, 6, 36, 216? What is the sum of the first 10 terms in the sequence 1, 6, 36, 216? What is the sum of the first n numbers in the sequence 1, 6, 36, 216?
In addition, we will also give you the formula that is used to calculate the next number or the nth number in 1, 6, 36, 216, and the formula to calculate the sum of n numbers in 1, 6, 36, 216.
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 1, 6, 36, 216? The sequence 1, 6, 36, 216 has a common ratio of 6 between each term. We call this kind of sequence a geometric sequence. Below is an image illustrating the correlation between the geometric sequence 1, 6, 36, 216 and its common ratio of 6.
Now, what is the next number in the sequence 1, 6, 36, 216? Below is the formula used to calculate the next number in a geometric sequence, such as 1, 6, 36, 216. 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 6. Furthermore, the next term in 1, 6, 36, 216 is the fifth term (5), and the first term is 1. When we enter these values into our formula, we get the following answer:
1 × 6^(5-1) = 1296
Thus, the next number (term) in the sequence 1, 6, 36, 216 is 1296. 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 1, 6, 36, 216, or 100 if you want the 100th term in the sequence 1, 6, 36, 216.
Let's move on to our next question. What is the sum of the first 10 terms in the sequence 1, 6, 36, 216? We use the formula below to calculate the sum of the first n terms in a geometric sequence such as 1, 6, 36, 216. 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 1, 6, 36, 216, as seen below:
(1 × (1 - 6^10)) ÷ (1 - 6) = 12093235
Therefore, the sum of all numbers up through the 10th term in the sequence 1, 6, 36, 216 is 12093235. 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 1, 6, 36, 216 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 1, 6, 36, 216.
Geometric Sequence Calculator
Go here to learn more about geometric sequences using the best online Geometric Sequence Calculator.
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