Also , given a list , we can tell if it is AP or not .
List 2,4,6,8,10 … here 4-2 = 6-4 = 8-6 = 10-8 = 2 , thus it is AP with common difference 2
List 1,3,4,6,7 , here 3-1 ≠ 4-3 , thus it is not AP . nth term of Arithmetic Progression
Let a1 , a2 , a3 , . . . be an AP whose first term a1 is a and the common difference is d ., thus the AP is a , a + d , a + 2d , a + 3d ,
So , the nth term an of the AP with first term ‘ a ’ and common difference d is given by an = a + ( n – 1 ) d .
an is also called the general term of the AP Operation on an A . P . :
( i ) If a constant is added to each term of an A . P ., the resulting sequence is also an A . P .
( ii ) If a constant is subtracted from each term of an A . P ., the resulting sequence is also an A . P .
( iii ) If each term of an A . P . is multiplied by a constant , then the resulting sequence is also an A . P .
( iv ) If each term of an A . P . is divided by a non-zero constant then the resulting sequence is also an A . P .
Example 1 : Find the 10th term of the AP : 2 , 7 , 12 , . . . Solution : Here , a = 2 , d = 7 – 2 = 5 and n = 10 . We have an = a + ( n – 1 ) d So , a10 = 2 + ( 10 – 1 ) × 5 = 2 + 45 = 47 Therefore , the 10th term of the given AP is 47 .