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### Finding the formula for a sequence of terms

Finding the formula for a sequence of terms
Finding the formula for a sequence of terms

### Expert Maths Tutoring in the UK 

Which formula can be used to describe the sequence below -8, -5, -2, 1, 4, …?. In an arithmetic sequence, the difference between any two consecutive terms is the same throughout the sequence.
(a_2) – (a_1) = -5 – (-8) = 3; (a_3) – (a_2) = -2 – (-5) = 3; …. Since the difference between every two consecutive terms is the same, the given sequence is an arithmetic sequence with d = 3.
Which formula can be used to describe the sequence below -8, -5, -2, 1, 4, …?. The formula to describe the sequence -8, -5, -2, 1, 4, ..

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An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. An arithmetic sequence can be defined by an explicit formula in which an = d (n – 1) + c, where d is the common difference between consecutive terms, and c = a1
The sum of an infinite arithmetic sequence is either ∞, if d > 0, or – ∞, if d

Then, the sum of the first n terms of the arithmetic sequence is Sn = n(). To use the second method, you must know the value of the first term a1 and the common difference d

### Expert Maths Tutoring in the UK 

What is the common ratio between successive terms in the sequence? 27, 9, 3, 1,…. A sequence in which the ratio between two consecutive terms is the same is called a geometric sequence.
The geometric sequence is generally represented in form a, ar, ar2, … where a is the first term and r is the common ratio of the sequence.
The common ratio of a geometric progression is calculated by dividing two consecutive terms and simplifying it to the simplest form.. In the sequence, the ratio 1/3 is the same and is called the common ratio.

### Expert Maths Tutoring in the UK 

Which formula can be used to describe the sequence below -8, -5, -2, 1, 4, …?. In an arithmetic sequence, the difference between any two consecutive terms is the same throughout the sequence.
(a_2) – (a_1) = -5 – (-8) = 3; (a_3) – (a_2) = -2 – (-5) = 3; …. Since the difference between every two consecutive terms is the same, the given sequence is an arithmetic sequence with d = 3.
Which formula can be used to describe the sequence below -8, -5, -2, 1, 4, …?. The formula to describe the sequence -8, -5, -2, 1, 4, ..

### Answered: Which formula can be used to describe… 

Which formula can be used to describe the sequence below? 27,9.3.1… Which formula can be used to describe the sequence below? 27,9.3.1..
Problem 3RE: Write the first four terms of the sequence defined by the explicit formula a an=10n+3 .. Problem 4RE: Write the first four terms of the sequence defined by the explicit formula an=n!n(n+1).
Problem 8RE: An arithmetic sequence has terms a3=11.7 and a8=14.6 . Problem 9RE: Write a recursive formula for the arithmetic sequence 20,10,0,10,…

### Describing Sequences 

You have a large collection of (1times 1) squares and (1times 2) dominoes. You want to arrange these to make a (1 times 15) strip
How are the (1times 3) and (1 times 4) strips related to the (1times 5) strips?. What if I asked you to find the number of (1times 1000) strips? Would the method you used to calculate the number fo (1 times 15) strips be helpful?
This is different from the set (N) because, while the sequence is a complete list of every element in the set of natural numbers, in the sequence we very much care what order the numbers come in. For this reason, when we use variables to represent terms in a sequence they will look like this:

### How to find the nth term of an arithmetic sequence 

Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence. The first term of an arithmetic sequence is ; the fifth term is
Example Question #2 : How To Find The Nth Term Of An Arithmetic Sequence. The sum of the first three terms of an arithmetic sequence is 111 and the fourth term is 49
Let be the common difference, and let be the second term. The fourth term is the second term plus twice the common difference:

### Geometric Sequences (Video) 

A geometric sequence is a list of numbers, where the next term of the sequence is found by multiplying the term by a constant, called the common ratio.. The general form of the geometric sequence formula is: (a_n=a_1r^{(n-1)}), where (r) is the common ratio, (a_1) is the first term, and (n) is the placement of the term in the sequence.
Then identify the first term, (a_1), which is (1). Therefore, the formula for this geometric sequence is (a_n=1·3^{(n-1)}).
Here is a geometric sequence: (2,10,50,250,1{,}250,…). Find the formula for the geometric sequence, then find the (7^{th}) term.

### Number patterns 

Write down the next three terms in each of the following sequences: (45; 29; 13; -3; ldots). – Emphasize the relationship between linear functions (general term) and linear sequences.
– Key activity in mathematical description of a pattern: finding the relationship between the number of the term and the value of the term.. In earlier grades we learned about linear sequences, where the difference between consecutive terms is constant
|Sequence/pattern||A sequence or pattern is an ordered set of numbers or variables.|. |Successive/consecutive||Successive or consecutive terms are terms that directly follow one after another in a sequence.|

### Number Sequence Calculator 

In mathematics, a sequence is an ordered list of objects. Accordingly, a number sequence is an ordered list of numbers that follow a particular pattern
In a number sequence, the order of the sequence is important, and depending on the sequence, it is possible for the same terms to appear multiple times. There are many different types of number sequences, three of the most common of which include arithmetic sequences, geometric sequences, and Fibonacci sequences.
A series is convergent if the sequence converges to some limit, while a sequence that does not converge is divergent. Sequences are used to study functions, spaces, and other mathematical structures

### Arithmetic Sequence Formula For Nth Term and Sum With Solved Examples 

Arithmetic sequence formula is used to calculate the nth term of an arithmetic sequence. To recall, a sequence is an ordered list of numbers
An arithmetic sequence or arithmetic progression is a sequence in which each term is created or obtained by adding or subtracting a common number to its preceding term or value. In other words, the difference between the adjacent terms in the arithmetic sequence is the same.
|Sum of First n Terms||Sn = n/2 (first term + last term)|. A few solved problems on the arithmetic sequence are given below.

### Introduction 

In this section we will cover basic examples of sequences and check on their boundedness and monotonicity. We start with alternating sequence and return to it again at the end, we briefly cover arithmetic sequences, but the most important type is the geometric sequence
An alternating sequence is actually a category, a more general type of a sequence (see the end of this section), but here we will look at the prototype alternating sequence:. From the picture we immediately see that this sequence is bounded (for all
This sequence appears quite often; sometimes by itself, more frequently as a part of another sequence; see the last section below.. By an arithmetic sequence we mean any sequence of the form

### Nth Term Of A Sequence 

One to one maths interventions built for KS4 success. Weekly online one to one GCSE maths revision lessons now available
Here we will learn about how to find the nth term of an arithmetic sequence. You’ll learn what the nth term is and how to work it out from number sequences and patterns.
We can make a sequence using the nth term by substituting different values for the term number(. To find the 20th term we would follow the formula for the sequence but substitute 20 instead of ‘

### Sequence and Series Formula 

We can define a sequence as an arrangement of numbers in some definite order according to some rule.. Think of patterns that you see around you in daily life
All of these can be determined and represented mathematically.. This mathematical representation of such patterns is studied under sequence and series.
We can commonly represent sequences as x1,x2,x3,……xn, where 1,2,3 are the positions of the numbers and n is the nth term.. Whereas, series is defined as the sum of sequences, which means that if we add up the numbers of the sequence, then we get a series.

### Sources

1. https://www.cuemath.com/questions/which-formula-can-be-used-to-describe-the-sequence-below-8-5-2-1-4/#:~:text=Summary%3A-,The%20formula%20to%20describe%20the%20sequence%20%2D8%2C%20%2D5%2C,..%20is%203n%20%2D%2011.
2. https://www.sparknotes.com/math/precalc/sequencesandseries/section2/#:~:text=An%20arithmetic%20sequence%20can%20be,%2C%20and%20c%20%3D%20a1.
3. https://www.cuemath.com/questions/what-is-the-common-ratio-between-successive-terms-in-the-sequence-27-9-3-1/#:~:text=Given%3A%20Sequence%20is%2027%2C%209,%2C%20ar2%2C%20…
4. https://www.cuemath.com/questions/which-formula-can-be-used-to-describe-the-sequence-below-8-5-2-1-4/
6. https://discrete.openmathbooks.org/dmoi3/sec_seq_intro.html
7. https://www.varsitytutors.com/algebra_1-help/how-to-find-the-nth-term-of-an-arithmetic-sequence