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Each number in a sequence is called a term. A sequence which increases or decreases by the same amount each time is called a linear sequence. Term to term rules. The term to term...
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GCSE; AQA; Sequences - AQA Test questions. Sequences can be...
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Simplifying rational close rational number A number that can...
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GCSE; AQA; Other graphs - AQA Quadratic graphs. The most...
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Here we will learn about different types of sequences including arithmetic sequences, geometric sequences and quadratic sequences and how to generate them and find missing terms, along with special sequences like the fibonacci sequence. We will also learn how to find the nth term of linear sequence and the nth term of a geometric sequence and ...
Free sequence calculator - step-by-step solutions to help identify the sequence and find the nth term of arithmetic and geometric sequence types.
Each number in a sequence is called a term. A sequence which increases or decreases by the same amount each time is called a linear sequence. It is useful to read the guides from M5 on...
- Ascending Order
- Descending Order
- Finite Sequence
- Infinite Sequence
- Arithmetic Sequence
- Quadratic Sequence
- Geometric Sequence
- Harmonic Sequence
- Triangular Number Sequence
- Square Number Sequence
If the elements of the sequence are in increasing order, then the order of the sequence is ascending. The above sequence is in ascending order as its terms are "increasing" by 2.
If the elements of the sequence are in decreasing order, then the order of the sequence is descending. The above sequence is in descending order as its terms are "decreasing" by 4. There are two types of sequences: finite sequences and infinite sequences. It is possible to count the number of terms in a finite sequence. An infinite sequence is a se...
A sequence having a finite number of terms is called a finite sequence. For example, a sequence of the number of bounces a ball takes to come to the rest is a finite sequence.
A sequence having an infinite number of terms is called an infinite sequence. For example, a sequence of natural numbersforms an infinite sequence: 1, 2, 3, 4, and so on. There are a few special sequences like arithmetic sequence, geometric sequence, Fibonacci sequence, harmonic sequence, triangular number sequence, square number sequence, and cube...
An arithmetic sequence is a sequence of numbers in which each successive term is a sum of its preceding term and a fixed number. This fixed number is called a common difference. The terms of the arithmetic sequence are of the form a, a+d, a+2d, .... Example:Mushi put $30 in her piggy bank when she was 7 years old. She increased the amount on her ea...
We have already seen that if the differences (referred to as first differences) between every two successive terms are the same, then it is called an arithmetic sequence (which is also known as a linear sequence). But if the first differences are NOT the same, and instead, the second differences are the same, then the sequence is known as a quadrat...
A geometric sequence is a sequence where every term bears a constant ratio to its preceding term. This ratio is called the "common ratio". The terms of the geometric sequence are of the form a, ar, ar2, .... Example:Consider an example of geometric sequence: 1, 4, 16, 64, .... Here, 4/1 = 16/4 = 64/4 = ... = 4. Hence, it is a geometric sequence wit...
A harmonic sequence is a sequence obtained by taking the reciprocalof the terms of an arithmetic sequence. Example:We know that the sequence of natural numbers is an arithmetic sequence. So, taking reciprocals of each term, we get 1, 1/2, 1/3, ..., which is a harmonic sequence as their reciprocals 1, 2, 3, ... form an arithmetic sequence.
A triangular number sequence is a sequence that is obtained from a pattern forming equilateral triangles. Look at the figure below. The sequence 1, 3, 6, 10, and so on is a triangular number sequence.
A square number sequence is a sequence that is obtained from a pattern forming squares. Look at the figure below. The sequence 1, 4, 9, 16, and so on is a square number sequence.
Once the first term and term to term rule are known, all the terms in the sequence can be found. Example 2. Work out the next two terms in the following sequence and write down the term to...
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Each number in the sequence is called a term. The first five terms of this sequence are 2, 4, 8, 16, and 32. Listing all of the terms for a sequence can be cumbersome. For example, finding the number of hits on the website at the end of the month would require listing out as many as 31 terms.