What is the sequence of 6 18 54 162?

The sequence 6, 18, 54, 162 is a geometric sequence with a common ratio of 3.

What kind of sequence is 6 18 54 162?

A geometric sequence (also known as a geometric progression) is a sequence of numbers in which the ratio of consecutive terms is always the same. For example, in the geometric sequence 2, 6, 18, 54, 162, …, the ratio is always 3. This is called the common ratio.

What is the rule for this sequence 6 18 54 162 486?

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 3 gives the next term. In other words, an=a1rn−1 a n = a 1 r n - 1 .

What number should come next in the sequence 2 6 18 54 162?

Which number comes next in the sequence: 2, 6, 18, 54, 162, 486, 1458, 4374, 13122, ..... My answer is 162.

What is the explicit formula for the sequence 2 6 18 54 162?

The explicit formula for the sequence 2, 6, 18, 54, 162 is an​=2(3)(n−1), which corresponds to option D. This sequence follows a geometric progression where each term is obtained by multiplying the previous term by 3.

Finding the next term of a sequence 486,162,54,18,6,...

What is the 7th term in the geometric sequence 2 6 18 54 162?

what is the 7th term? -2(-3)^(n - 1) n=1,2,3,4,5,6,7 -2,6,-18,54,-162,486,-1458 7th term -2(-3)^6 = -1458 Definition geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.

What number comes next in the sequence 2 6 18 54?

The next number in the series? -2, 6, 18, 54, ... is 162. To find the answer, we need to determine the pattern.

What is a recursive rule for the geometric sequence 6 − 18 54 − 162?

The recursive rule for the geometric sequence 6,−18,54,−162,... is defined with the first term a1​=6 and the rule an​=−3⋅an−1​ for n≥2. This captures the constant ratio of −3.

What number is missing in the pattern 486 162 54 _____ 6?

The given sequence is 486, 162, 54, 18, 6.

Which term of the sequence 2 6 18 54 is 486?

Answer: -486 is the 6th term of the sequence.

What's the recursive formula of the geometric sequence below 2 6 18 54 162 486?

The recursive formula for the geometric sequence 2, 6, 18, 54, 162, 486, ... is a1=2;an=an−1⋅3 for n≥2.

What number is missing in the pattern 2 6 54 162?

The missing number in the pattern 2, 6, __, 54, 162 is 18, making the complete sequence 2, 6, 18, 54, 162.

What is the common ratio of the geometric sequence 2 6 18 54 1 point?

Summary: The common ratio of the sequence -2, 6, -18, 54 ….. is -3.

What kind of sequence is this 6 18 54 162?

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 3 gives the next term. In other words, an=a1rn−1 a n = a 1 r n - 1 .

How do you write a recursive rule for a sequence?

First, identify the common difference (how much each term in a sequence is increasing or decreasing from the previous term). State the first term of the sequence, and then write the recursive rule as (new term) = (previous term) + (common difference).

What is the recursive rule for the sequence 1 − 6 36 − 216 responses?

The recursive rule for the sequence 1, -6, 36, -216, ... is n × − 6 . The recursive rule for the given sequence is n × − 6 , in which n represents the value of the term just prior to the term in question. We can see this when we multiply 1 by -6 to get -6, then when we multiply -6 by -6 to get 36 and so on.

What is the next number in the sequence 2 6 18 54 162?

This is a geometric sequence (a sequence with a common ratio which takes the nth term of ar^n-1). Here, the nth term is 2 x 3^n-1. Therefore, the next term, term 7, is 2 x 3^7–1 = 1458.

How can I find the nth term?

To find the nth term, first identify the sequence type (usually arithmetic), find the common difference (dd𝑑), and use the formula an=a1+(n−1)da sub n equals a sub 1 plus open paren n minus 1 close paren d𝑎𝑛=𝑎1+(𝑛−1)𝑑 (for arithmetic), where a1a sub 1𝑎1 is the first term, or use the shortcut of finding the pattern d×nd cross n𝑑×𝑛 and adjusting by adding/subtracting a constant to match the sequence, giving a form like dn+cd n plus c𝑑𝑛+𝑐.
 

What is the explicit formula for the geometric sequence 2 6 18 54?

So, the explicit formula for the given geometric sequence is: a n = 2 ⋅ 3 ( n − 1 )

How to determine a sequence?

An arithmetic sequence is a number pattern where the rule is addition or subtraction. To create the rule, look for the common difference between the terms and then decide if the terms are going up or down. The rule should be general enough that it helps you find the next terms of the sequence.

What are odd and even numbers Grade 3?

A number is even if it ends in 2, 4, 6, 8, or 0. A number is odd if it ends in 1, 3, 5, 7, or 9.

Is the Fibonacci sequence arithmetic or geometric?

Earlier, you were asked if all sequences are arithmetic or geometric. The sequence above shows that not all sequences are arithmetic or geometric. Two famous sequences that are neither arithmetic nor geometric are the Fibonacci sequence and the sequence of prime numbers.