Any pair of numbers will always form an arithmetic sequence.
Yes.
One of the simplest arithmetic arithmetic sequence is the counting numbers: 1, 2, 3, ... . The person who discovered that is prehistoric and, therefore, unknown.
It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence. The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
It is the start of an arithmetic sequence.
Goemetric sequence : A sequence is a goemetric sequence if an/an-1is the same non-zero number for all natural numbers greater than 1. Arithmetic sequence : A sequence {an} is an arithmetic sequence if an-an-1 is the same number for all natural numbers greater than 1.
Any pair of numbers will always form an arithmetic sequence.
A single number, such as 11111, cannot define an arithmetic sequence. On the other hand, it can be the first element of any kind of sequence. On the other hand, if the question was about ``1, 1, 1, 1, 1'' then that is an arithmetic sequence as there is a common difference of 0 between each term.
The nth term of an arithmetic sequence = a + [(n - 1) X d]
Yes.
One of the simplest arithmetic arithmetic sequence is the counting numbers: 1, 2, 3, ... . The person who discovered that is prehistoric and, therefore, unknown.
origin of arithmetic sequence
It is an arithmetic sequence for which the index goes on and on (and on).
It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence. The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
It is an arithmetic sequence (with constant difference 0), or a geometric sequence (with constant ratio 1).