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.