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 , .........

What should come in the place of Question marks (?) in the following series?

1) 3 , 8 , 15 , 24 , ? , 48 ,63

3 , 8 , 15 , 24 , ? , 48 , 63

3 , 3+5 , 8+7 , 15+9 , ? , ?+? , 48+15
as we see odd numbers are added to the previous numbers in increasing order.

3 , 3+5 , 8+7 , 15+9 , 24+11 , 35+13 , 48+15

so the answer is 35 and final series is -

3 , 8 , 15 , 24 , 35 , 48 , 63


2) 3 , 4 , 8 , 17 , 33 , ? ,94

3 , 4 , 8 , 17 , 33 , ? ,94

3 , 3+12 , 4+22 , 8+33 , 17+42, ?+? , ?+?
as we see the sequence .

3 , 3+12 , 4+22 , 8+33 , 17+42, , 33+52 , 58+62

so the answer is 58 and final series is -

3 , 4 , 8 , 17 , 33 , 58 ,94


3) 1/12 , 1/6 , 1/4 , 1/3 , ? ,1/2

lets take the LCM -

1, 2, 3, 4 , 5 , 6 /12
as we see the sequence .

1/12 , 2/12 , 3/12 , 4/12 , 5/12 , 6/12

so the answer is 5/12 and final series is -

1/12 , 2/12 , 3/12 , 4/12 , 5/12 , 6/12


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