Arithemetric Progression Help?

a,b,c,d are said to be in AP if b-a = c-b = d-c = cd ( common difference )

1) 1,5,9,13

here, 5-1 = 9-5 = 13-4 = 4 .. hence this is an AP and cd = 4

2) 1,2,4,8

2-1 != 4-2 != 8-4 .... not an AP .. ( != means not equal to ) [ it is a GP btw ]

3) 3-7 = -1-3 = -5+1 = -4 .... AP with cd = -4

4) 1/3 - 1/2 != 1/4 - 1/3 != 1/5 - 1/4 ... not an AP .. but its reciprocals are in AP, hence it is a HP

5) 3/4 - 3/8 = 9/8 - 3/4 = 3/2 - 9/8 = 3/8 ... hence AP with cd = 3/8

An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant.

In the first sequence,
5 - 1 = 4
9 - 5 = 4
3 - 9 = -6
Hence, it is not an arithmetic progression.

In the second,
2 - 1 = 1
4 - 2 = 2
Hence, it is not an arithmetic progression.

In the third,
3 - 7 = -4
-1 - 3 = -4
-5 - (-1) = -4
Hence, it is an arithmetic progression, with -4 as the common difference.

In the fourth,
1/3 - 1/2 = -1/6
1/4 - 1/3 = -1/12
Hence, it is not an arithmetic progression.

In the fifth,
3/4 - 3/8 = 3/8
1 1/8 - 3/4 = 3/8
1 1/2 - 1 1/8 = 3/8
Hence, it is an arithmetic progression, with 3/8 as the common difference.