Identify the Sequence 3 , 6 , 9 , 12
Step 1
This is an arithmetic sequence since there is a common difference between each term. In this case, adding to the previous term in the sequence gives the next term. In other words, .
Arithmetic Sequence:
Step 2
This is the formula of an arithmetic sequence.
Step 3
Substitute in the values of and .
Step 4
Step 4.1
Apply the distributive property.
Step 4.2
Step 5
Combine the opposite terms in .
I'm here to provide expert insights and knowledge on the topic at hand. As someone well-versed in mathematics, particularly algebra and sequences, I can confidently address the concepts mentioned in the article you provided.
The sequence 3, 6, 9, 12 is identified as an arithmetic sequence, where there is a common difference between each term. In this case, adding 3 to the previous term in the sequence results in the next term. The general formula for an arithmetic sequence is given by:
[a_n = a_1 + (n-1)d]
Here, (a_n) is the nth term, (a_1) is the first term, (n) is the position of the term in the sequence, and (d) is the common difference.
The article outlines the steps to identify and work with this arithmetic sequence. Let's break down each step:
Step 1:
Identify the sequence as an arithmetic sequence due to the common difference.
Step 2:
Introduce the formula for an arithmetic sequence:
[a_n = a_1 + (n-1)d]
Step 3:
Substitute the given values of (a_1) and (d) into the formula.
Step 4:
Simplify each term in the formula.
Step 4.1:
Apply the distributive property.
Step 4.2:
Multiply by the given values.
Step 5:
Combine opposite terms in the formula.
Step 5.1:
Subtract one term from another.
Step 5.2:
Add and combine terms.
By following these steps, you can manipulate and simplify the arithmetic sequence. If you have specific questions or if there's a particular aspect you'd like me to delve into further, feel free to ask!
FAQs
This is an arithmetic sequence since there is a common difference between each term. In this case, adding 3 to the previous term in the sequence gives the next term.
What kind of sequence is this 3 6 9 12? ›
The nth terms: 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 , 30 , 33...
What is the missing term of 3 6 9 12? ›
The next number in the sequence is 15. The pattern in this sequence is that each term is obtained by adding 3 to the previous term. So, starting with 3 and adding 3 repeatedly, we get: 3, 3 + 3 = 6, 6 + 3 = 9, 9 + 3 = 12, 12 + 3 = 15, and so on.
What is the rule for the sequence 3 6 12? ›
The nth term of the sequence can be solved using the formula a n = 3 ⋅ 2 n − 1 . To elaborate, the sequence 3, 6, 12, 24, ... is a geometric sequence with a common ratio of 2.
What is the 20th term of the sequence 3 6 9 12? ›
Answer. Answer: The 20th term is 60.
How many terms are there in sequence 3 6 9 12? ›
Thus, the given sequence contains 37 terms.
How many terms should be added in the sequence 3 6 9 12 to sum up to 165? ›
Expert-Verified Answer
we need to find the number of terms of the given AP for which its sum is 165. Thus, the number of terms for which the given AP's sum is 165 is 10.
Is 3,6,9,12 ap give reasons? ›
Since the difference between the two consecutive terms of the given series is not same, thus the given series is not an arithmetic progression. Was this answer helpful?
What is the missing term of the sequence 3 6 12 24 rule? ›
To find the next number in the sequence, we can see that each number in the sequence is being multiplied by 2 to obtain the next number. Therefore, the next number in the sequence is 96. So the complete sequence is: 3, 6, 12, 24, 48, 96...
What is the nth term of the sequence 3 6 9? ›
3, 6, 9, 12, … =3*1, 3*2, 3*3, 3*4, … So the next three terms are 3*5=15, 3*6=18, 3*7=21. The general formula of this sequence is a_n=3*n, n=1, 2, 3 …
The 12th term of the sequence 3, 6, 12, 24,.. is a12 = 6144.
Is 3 6 12 arithmetic or geometric? ›
In contrast, a geometric sequence is one where each term equals the one before it multiplied by a certain value. An example would be 3, 6, 12, 24, 48, …
Is 3, 6, 12, 24 an arithmetic sequence? ›
Answer and Explanation:
No, 3, 6, 12, 24, . . . is not an arithmetic sequence. An arithmetic sequence is defined as a sequence in which the difference between each consecutive term is constant.
How many terms of the progression 3 6 9 12 must be taken at the least to have a sum not less than 2000? ›
So, this should be around 2000, that is n2 should be around 2/3⋅2000≈1334. Using calculator, its square root is ≈36.52 and substituting n=36 to S(n) gives S(36)=1998, so at least 37 terms are needed to exceed 2000.
What is the sequence of 6 12 20? ›
The sequence becomes 2, 6, 12, 20, 30, 42, 56. Note: We used the term 'prime numbers' in the solution. Prime numbers are the numbers which have only two factors, 1 and the number itself. For example: 2 is the product of 2 and 1.
How many terms of the sequence 12 9 6 3 should be taken so that their sum is zero? ›
or N^2 - 9*N - 36 = 0. or (N - 12)*(N + 3) = 0. or N = 12 [Ans]
What is the sequence of 3 6 9? ›
3, 6, 9, 12, … =3*1, 3*2, 3*3, 3*4, … So the next three terms are 3*5=15, 3*6=18, 3*7=21. The general formula of this sequence is a_n=3*n, n=1, 2, 3 …
What type of sequence is 3 9 15 21? ›
For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6. An arithmetic sequence can be known as an arithmetic progression. The difference between consecutive terms is an arithmetic sequence is always the same.
What type of sequence is 3 5 7 9 11? ›
An arithmetic progression is a sequence where each term is a certain number larger than the previous term. The terms in the sequence are said to increase by a common difference, d. For example: 3, 5, 7, 9, 11, is an arithmetic progression where d = 2. The nth term of this sequence is 2n + 1 .
What type of sequence is 3 5 9 15 23? ›
Because the second level difference is constant, the sequence is quadratic and given by an=an2+bn+c a n = a n 2 + b n + c .
