Arithmetic Progression is sequence of numbers that increase or decrease by a common difference such that any number in the sequence is the average (arithmetic mean) of the numbers preceding and following it.
Example the following numbers form an arithmetic progression
2, 4, 6, 8, 10, 12, 14
the common difference d is 2 while the first term is 2
The common difference can be found by finding the difference between a term in the sequence and the preceding term eg from above 4 - 2 = 2
The general arithmetic progression from the above is
a, a + d, a + 2d, a + 3d, ...... where the first term, a and the common diference are arbitary numbers. The nth term of this progression is given by the formula
Tn = a + (n - 1)d.
Sum of Arithmetic Progression
To find the sum ofany arithmetic progression can be found by multiplying the sum of the first and last terms by half the number of terms. Eg the sum of the arithmetic progression of first ten natural numbers - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is (1 + 10) x (10 / 2) = 55
Therefore the formula for the first n terms of an arithmetic progression is
n/2[2a + (n - 1)d] 07 September 2010Comment