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 2 gives the next term. In other words, an=a1⋅rn−1 a n = a 1 ⋅ r n - 1 . This is the form of a geometric sequence.

Similarly one may ask, what is the next number in the sequence 3 6 12?

12 - (9-1)= 12 - 8= 4. 4 + 2(9-1) = 4+ 2(8) = 4 + 16= 20. If we put those answers in order, we have 3, -6, 12, 4, 20: the original sequence!

Furthermore, what is the next number in the sequence 12 24 48? One answer is the sequence 12, 24, 48, found by John. The second answer is the sequence 4, -8, 16. The three terms are a, ar and ar^2.

Also know, which is the equation for the nth term of the geometric sequence 6 12 24?

Question 1086787: in the geometric sequence 6,12,24,48, which term is 768? The n-th term of a geometric sequence is a_n = a*r^(n-1) where r is the common ratio and a is the 1st term. In this case, r = 2, and the 1st term is 6.

What is the nth term in a sequence?

a₄ = a₃ + d = (a₁ + 2d) + d = a₁ + 3d. Capturing this pattern in alegbra, we write the general (or nth) term of an arithmetic sequence as: a_n = a₁ + (n - 1 ) d. This is the formula that will be used when we find the general (or nth) term of an arithmetic sequence.

Related Question Answers

What is the common ratio of the geometric sequence 3 6 12 24?

2

What is the common ratio of the sequence 3 6 12?

Common ratio is 2 .

What kind of sequence is 6 18 54?

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 difference between an arithmetic sequence and geometric sequence?

An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.

Where can you apply geometric sequence?

Geometric series are used throughout mathematics. They have important applications in physics, engineering, biology, economics, computer science, queueing theory, and finance.

What is a common ratio in a geometric sequence?

A geometric sequence is one in which any term divided by the previous term is a constant. This constant is called the common ratio of the sequence. The common ratio can be found by dividing any term in the sequence by the previous term.

How do you find the next term in a geometric sequence?

A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. So 1, 2, 4, 8, 16, is geometric, because each step multiplies by two; and 81, 27, 9, 3, 1, 31 , is geometric, because each step divides by 3.

What is the 5th term of the geometric sequence 3 20?

1,500

What is the sixth term of the geometric sequence?

The sixth term of the geometric sequence is a6=1,701 a 6 = 1 , 701 .

Is the sequence geometric if so identify the common ratio 6 12 24?

If so, identify the common ratio. 6, 12, 24, 48, yes; 2.

Which sequence has a common ratio of?

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio. For example, the sequence 2, 6, 18, 54, is a geometric progression with common ratio 3.

What is the next term in the geometric sequence 4/12 36?

Answer Expert Verified

The answer is -108. Based on the given geometric sequence, the next term is -108. The given in the geometric sequence are: 4, -12, 36.

What is the common ratio of sequence 3/12 48?

Explanation: The given sequence is geometric, with the common ratio being 4 and the first term being 3.

What is the common ratio?

more The amount we multiply by each time in a geometric sequence. Example: 1, 2, 4, 8, 16, 32, 64, 128, 256, Each number is 2 times the number before it, so the Common Ratio is 2.

Where can you apply the concepts and skills that you learned about geometric sequence?

Answer. Answer: You can apply geometric sequences and series to different physical and mathematical topics. Geometric series played an important role in the early development of calculus, and continue as a central part of the study of the convergence of series.

What is the relation or formula for an arithmetic sequence?

An arithmetic sequence can be defined by an explicit formula in which a_n = d (n - 1) + c, where d is the common difference between consecutive terms, and c = a₁. Then, the sum of the first n terms of an arithmetic sequence is S_n = na₁ + (dn - d ).

What is the 5th term of the arithmetic sequence an 5n 1?

Answer: A5 =26. Step-by-step explanation: An =5n+1. A5=5(5)+1.

What is the common ratio for the sequence 3/15 75?

So, the common ratio is 5.

Which of the following is a geometric sequence?

Sequences of numbers that follow a pattern of multiplying a fixed number from one term to the next are called geometric sequences. The following sequences are geometric sequences: Sequence A: 1 , 2 , 4 , 8 , 16 ,

What is the 10th term of arithmetic sequence an 3n 5?

Answer: The 10th term is 25.

What is the 10th term of the arithmetic sequence?

10=a10=a1+9d=−17+9d. ⇒9d=27. ⇒d=3. Thus the first term is −17 and the common difference is 3 .

How do I write the nth term?

The 'nth' term is a formula with 'n' in it which enables you to find any term of a sequence without having to go up from one term to the next. 'n' stands for the term number so to find the 50th term we would just substitute 50 in the formula in place of 'n'.

What is the nth term examples?

Usually, it will look something like "n+1", or "3n-5". For example, work out the nth term for the linear sequence "2, 5, 8, 11, ". We can see that the common difference is 3 [Can you see this? 5-2=3, 11-8=3 etc.].

How do you find a term in a sequence?

To find the "nth" term of an arithmetic sequence, start with the first term, a(1). Add to that the product of "n-1" and "d" (the difference between any two consecutive terms). For example, take the arithmetic sequence 3, 9, 15, 21, 27. a(1) = 3. d = 6 (because the difference between consecutive terms is always 6.

How do you calculate a sequence?

The general formula for any sequence involves the letter n, which is the position of the term in the sequence (the first term would be n = 1, and the 20th term would be n = 20), as well as the rule to find each term.

What is the sequence for 25 3n?

Hence the three terms of 25–3n are 22, 19 and 16.