Logical 11 - Sequences and Series

Key Points to Remember:

Sequences and series consists of questions where we are supposed to understand the logic behind a given sequence or series of number/alphabets. Based on this understanding we are supposed to determine either:

(a) A continuation to the series

(b) The immediate next term of the series

or

(c) A missing term/terms within the series.

We should improve our ability to spot a particular relationship between terms within the series. The common logical premises used for questions are given here.

SERIES BASED ON NUMBERS

1. Squares

2. Squares + something or squares–something e.g. next term in the series 24, 35, 48, 63, 80... will be 99 since the series is (52 + 1), (62 + 1), etc.

3. Cubes, cubes + something, cubes–something

4. Geometric series

5. Arithmetic series

6. Harmonic series

7. Series of constantly changing additions or multiplications, e.g.,

(i) 2, 6, 24, 120,.......... (The terms are got by ¥ 3, ¥ 4, ¥ 5, and so on.)

(ii) 11, 16, 22, 29, 37,.......... (The series follows a logic of +5, +6, +7, +8, and so on.)

8. Binary numbers systems or number systems with other bases like Base 3, Base 4, etc.

9. Intermingled series–

e.g., 2, 5, 6, 10, 18, 15, 54

In this series alternate terms starting with the first form a GP with common ratio 3, while the 2nd, 4th, 6th terms form an AP 5, 10, 15.........

SERIES BASED ON ALPHABETS

In such series, the most crucial aspect is to know the position of each alphabet in the alphabet series

A to Z both from start to end.

Thus, the following reference numbers for each alphabet become important:

Notice that M and N are the two middle points of this series.

Practice Questions:

Question 1:

Which of the following letters would come next in the series of letters?

Z, W, R, K, __

(a) A 

(b) C

(c) B 

(d) D

In the given series from the end of the alphabet series, Z is the 1st alphabet, W is the 4th alphabet, R is the 9th alphabet and K is the 16th alphabet. Thus the next letter in the series will be the 25th alphabet from the end or the second from the start. Hence, the next alphabet must be B. Thus (c) is the correct option.

Question 2:

0.005, 0.05, ?, 5

(a) 5.50 

(b) 0.05

(c) 0.5 

(d) none of these

A Geometric Progression with common ratio 10. Hence, the missing term will be 0.5 i.e., option (c).

Question 3:

What would come next in the following series?

A10, D15, G20, J25 __

(a) N18 

(b) O20

(c) M16 

(d) none of these

In the series of letters represented above there is a gap of 2 letters between every two consecutive terms and hence, the next letter will be M (after skipping K and L). Thus, the correct answer should be M30. Thus Option (d) is correct.

Question 4:

(1, 1), (2, 16), (3, 81), ?

(a) (4, 16) 

(b) (4, 64)

(c) (4, 256) 

(d) none of these

The relationship followed in each bracket is the fourth power of the first digit in the bracket. Hence, option (c) is correct.

Question 5:

ABCDEFG, GABCDEF, FGABCDE, ?

(a) EFGABCD 

(b) GABCDEF

(c) EFGABCDE 

(d) FGABCDE

The next term is formed by removing the last alphabet in the previous term and attaching it to the first alphabet of the next term. Hence, the next term in the series would be EFGABCD. So, the answer is option (a).

Time to Think:

What is the next term in the following series?

1, 4, 3, 9, 5, 16, 7, 25, 9, 36, 11, ?

(a) 64 

(b) 49

(c) 48 

(d) 55