The sequence 1, 4, 9, 16, and so on is a square number sequence. Square Number SequenceĪ square number sequence is a sequence that is obtained from a pattern forming squares. The sequence 1, 3, 6, 10, and so on is a triangular number sequence. Triangular Number SequenceĪ triangular number sequence is a sequence that is obtained from a pattern forming equilateral triangles. , which is a harmonic sequence as their reciprocals 1, 2, 3. So, taking reciprocals of each term, we get 1, 1/2, 1/3. Harmonic SequenceĪ harmonic sequence is a sequence obtained by taking the reciprocal of the terms of an arithmetic sequence.Įxample: We know that the sequence of natural numbers is an arithmetic sequence. Hence, it is a geometric sequence with common ratio 4. Įxample: Consider an example of geometric sequence: 1, 4, 16, 64. The terms of the geometric sequence are of the form a, ar, ar 2. This ratio is called the " common ratio". Take a look at the figure below.Ī geometric sequence is a sequence where every term bears a constant ratio to its preceding term. is a quadratic sequence because their second differences are the same. But if the first differences are NOT the same, and instead, the second differences are the same, then the sequence is known as a quadratic sequence.Įxample: The sequence 1, 2, 4, 7, 11. 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). This fixed number is called a common difference. The succeeding terms are obtained by adding a fixed number, that is, $3. So, the amount in her piggy bank follows the pattern of $30, $33, $36, and so on. She increased the amount on her each successive birthday by $3. Įxample: Mushi put $30 in her piggy bank when she was 7 years old. The terms of the arithmetic sequence are of the form a, a+d, a+2d.
Arithmetic SequenceĪn arithmetic sequence is a sequence of numbers in which each successive term is a sum of its preceding term and a fixed number. We will discuss these sequences in detail. and this sequence does not belong to any of the following sequences. is a sequence in which the numbers can be written as 1 3 + 1, 2 3 + 1, 3 3 + 1, 4 3 + 1.
Apart from these, there can be sequences that follow some other pattern. There are a few special sequences like arithmetic sequence, geometric sequence, Fibonacci sequence, harmonic sequence, triangular number sequence, square number sequence, and cube number sequence.
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