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: n²+n. Next number kya hai? (Sirf number)

Common mistakes

Sirf addition check karna: Pehle difference dekho, nahi mila toh ratio dekho, phir squares/cubes dekho. Multiple patterns try karo.
Wrong number mein pattern galat pehchanna: Pura pattern identify karo pehle, phir kaunsa number break kar raha hai wo nikalo.
Alternating series miss karna: Agar difference consistent nahi hai, toh odd/even positions alag check karo.
Zyada complex sochna: Pehle simple patterns try karo — addition, subtraction, multiplication. Complex baad mein.

Lesson complete?

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