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An arithmetic progression is a sequence in which each term after the first is formed by adding a fixed amount, called the common difference, to the preceding term.
If a is the first term, d is the common difference, and n is the number of terms an arithmetic progression, the successive terms are
a, a + d, a + 2d, a + 3d,….a + (n-1)d
Thus, the last term (or nth term) l is given by
l= a + (n - 1)d
The sum S of the n terms of this progression is given by
between the first and last terms of an arithmetic progression are called
arithmetic means between these two terms. Thus to insert k arithmetic
means between two numbers is to form an arithmetic progression of (k+2)
terms having the two given numbers as the first and the last terms.
geometric progression is a sequence in which each term after the first is
formed by multiplying the preceding term by a fixed number, called the
If a is
the first term, r is the common ratio, and n is the number of terms, the
geometric progression is:
a∙r, a∙r2, ….. a∙rn-1
last ( or nth ) term l is given by l = a∙rn-1.
The sum S
of the first n terms of the geometric progression is given by:
between the first and the last terms of a geometric progression are called
geometric means between two terms. Thus, to insert k geometric means
between two numbers is to form a geometric progression of k+2 terms having
the two given numbers as the first and last terms.
"Chance favors the prepared mind." - Louis Pasteur