Quantities are said to be in arithmetic progressions (A.P.) when they increase or decrease by a common difference.
E.g. I. 3, 7, 11, 15…..
II. 8, 2, -4, -10…..
III. a, a+d, a+2d, a+3d…..
Common difference: The common difference (d) is found by subtracting any term of the series from the next term.
E.g. in I. d = 7-3 = 4
In II. d = 2-4 = -6
In III. d = a+d – d = a
- The nth term of an arithmetic progression is given by:
Tn = a + (n-1) d
Where a is the first term of the series, d is the common difference and n is the number of terms.
- If n be the number of terms, and if L denotes the last term or nth term than
L = a + (n-1) d