# Series and Sequences

## Types of Series :

### Arithmetic Progression (A.P.) -

a , a + d , a + 2d , a + 3d , ......., a + (n-1)d
Where a = First Term , d = Comman Difference and n = Number of Terms
Example - 1,4,7,10,..........

### Geometric Progression (G.P.) -

a , a r , a r2, a r3, ......., a r(n-1)
Example - 4 , 4*2 , 4*22 , 4*23 , .........
4 , 8 , 16 , 32 .........

### Harmonic Progression (H.P.) -

1 / a , 1 / (a + d) , 1 / (a + 2d) , 1 / (a + 3d) , ......., 1 / a + (n-1)d
Example - 1/1 , 1/4 , 1/7 , 1/10 ,..........

### Sequences Of Square -

a2 , b2 , c2 , .......... , n2
Example - 12 , 22 , 32 , .......... , n2

### Sequences Of Qube -

a3 , b3 , c3 , .......... , n3
Example - 13 , 23 , 33 , .......... , n3

### Sequences Of Prime Number -

Example - 2 , 3 , 5 , 7 , 11 , ..........

### Arithmetic - Geometric sequences -

Example - 1 , 6 , 21 , 66 , ..........
1 , (1+1)3 , (6+1)3 , (21+1)3 , .........

### Geometric - Arithmetic sequences -

Example - 2 , 8 , 26 , 80 , ..........
2 , (2*3)+2 , (8*3)+2 , (26*3)+2 , .........

### Sequence containing two sequences-

Example - 4 , 7 , 8 , 9 , 12 , 11 , 16 , 13 , ....
first sequence - 4 , 8 , 12 , 16 , .........
second sequence - 7 , 9 , 11 , 13 , .........