Learn�Aptitude�Reasoning & Data Interpretation

Lesson 6 � Intermediate

Number Series & Patterns

Number series reasoning ka sabse common topic hai. Har exam mein 3-5 questions aate hain. Pattern pehchanna seekho � arithmetic, geometric, square, cube sab cover karenge.

? 20 min✓ Intermediate✓ Basic arithmetic

Series ke types

WHAT

Number series mein ek sequence hota hai with a hidden logic. Tumhe wo logic pehchanna hai aur missing/wrong number nikalna hai. Jaise 2, 4, 8, 16, ? � ye geometric hai, answer 32.

WHEN

TCS, Infosys, Wipro sab mein aata hai. Usually 3-5 questions hote hain. 30 seconds mein solve karna hai � pattern pehchano aur answer do.

WHERE

Differences dekho, ratios dekho, squares/cubes dekho. Pehle simple patterns check karo (addition, subtraction), phir complex (multiplication, powers).

Strategy: Pehle consecutive terms ka difference nikalo. Agar difference constant hai � arithmetic. Agar ratio constant hai � geometric. Agar nahi hai � squares, cubes, ya alternating pattern check karo.

Arithmetic Series

# Arithmetic: Common difference hota hai
# 3, 7, 11, 15, 19, ? ✓ d = 4, answer = 23

# Increasing difference:
# 2, 3, 5, 8, 12, ?
# Differences: 1, 2, 3, 4 ✓ next = 5
# Answer = 12 + 5 = 17

# Second-level difference:
# 1, 2, 4, 7, 11, ?
# 1st diff: 1, 2, 3, 4
# 2nd diff: 1, 1, 1 ✓ constant
# Next 1st diff = 5
# Answer = 11 + 5 = 16

# Alternating series:
# 2, 5, 3, 6, 4, ?
# Odd positions: 2, 3, 4 ? +1
# Even positions: 5, 6 ? +1
# Answer (6th position) = 6 + 1 = 7

Geometric & Power Series

# Geometric: Common ratio hota hai
# 3, 6, 12, 24, 48, ? ✓ r = 2, answer = 96

# Squares:
# 1, 4, 9, 16, 25, ? ? 1�, 2�, 3�, 4�, 5� ✓ answer = 36

# Cubes:
# 1, 8, 27, 64, 125, ? ? 1�, 2�, 3�, 4�, 5� ✓ answer = 216

# Squares +/- constant:
# 0, 3, 8, 15, 24, ? ? 1�-1, 2�-1, 3�-1, 4�-1, 5�-1 ✓ answer = 35

# Powers of 2:
# 1, 2, 4, 8, 16, 32, ? ✓ answer = 64

# Mixed operations:
# 1, 2, 6, 24, 120, ? ? 1!, 2!, 3!, 4!, 5! ✓ answer = 720

Complex patterns

# Pattern 1: Multiply then add
# 2, 5, 11, 23, 47, ?
# �2+1: 2�2+1=5, 5�2+1=11, 11�2+1=23, 23�2+1=47
# Answer = 47�2+1 = 95

# Pattern 2: Square then add index
# 0, 2, 6, 12, 20, ?
# 0�0+0=0, 1�1+1=2, 2�2+2=6, 3�3+3=12, 4�4+4=20
# Answer = 5�5+5 = 30

# Pattern 3: Product of previous terms
# 1, 1, 2, 3, 6, ?
# Each = product of previous two
# 1, 1, 1�1=1, wait...
# Better: 1, 2, 3, 6, 18, ?
# 1�2=2, 2�3=6, 3�6=18... no
# Actually: 1, 2, 3, 6, 11, ?
# Diff: 1, 1, 3, 5... odd numbers
# Next diff = 7, answer = 11+7 = 18

# Pattern 4: Digit operations
# 121, 144, 169, 196, ? ? 11�, 12�, 13�, 14� ✓ answer = 225
Pro Tip: Agar 5 numbers diye hain aur pattern samajh nahi aa raha, toh last number ko check karo � kya wo wrong hai✓ Wrong number finding mein pattern same hota hai bas ek number galat hota hai.

Wrong Number Finding

Ismein series mein ek number galat hota hai. Wahi nikalna hai:

# Example: 2, 6, 12, 20, 30, 42
# Differences: 4, 6, 8, 10, 12 ✓ correct pattern
# All correct � no wrong number

# Example: 2, 6, 14, 20, 30, 42
# Differences: 4, 8, 6, 10, 12 ✓ pattern broken at 14
# Should be: 2, 6, 12, 20, 30, 42
# Wrong number = 14 (should be 12)

# Strategy for wrong number:
# 1. Differences nikalo
# 2. Pattern identify karo
# 3. Jo term pattern break kare � wo wrong hai
# 4. Verify karo: uske baad ka pattern bhi check karo

Exercise

Question: Series: 2, 4, 8, 16, ? � Next number kya hai? (Sirf number)

Question: Series: 1, 4, 9, 16, ? � Next number kya hai? (Sirf number)

Question: Series: 2, 5, 11, 23, 47, ? � Pattern: �2+1. Next number kya hai? (Sirf number)

Question: Series: 0, 2, 6, 12, 20, ? � Pattern: n�+n. Next number kya hai? (Sirf number)

Common mistakes

Lesson complete?

Number series samajh aa gaya✓ Ab Logical Reasoning seekhte hain � blood relations, seating arrangement, syllogisms.