⇒ Arithmetic Progression: A sequence of numbers in which the successive terms increase or decrease by a constant number is called an “Arithmetic Progression (AP)”
⇒ Common Difference: The constant difference between two consecutive terms of an AP is called “Common Difference”.
⇒ General Form of an AP: If the first term is ‘a’ and common difference is ‘d’, then a, a + d, a + 2d, a + 3d,... represent the arithmetic progression for different values of ‘a’ and ‘d’. This is called “General Form of an AP”
⇒ nth term of an A.P.: The nth term of an AP is given by:
an = a + (n - 1)d.
⇒ Sum of first n -terms of an AP: If a, a + d, a + 2d, ... is an AP and nth term an = a+(n-1) d. Then, the sum of n-terms is:
where a = First term of an AP
l = Last term of an AP = a + (n-1) d