Multiplication and Division Series

If a series grows rapidly, divide consecutive terms instead of subtracting. A constant ratio means geometric (e.g., 3, 6, 12, 24 — ×2). Often the multiplier itself changes: 1, 2, 6, 24, 120 multiplies by 2, 3, 4, 5. Speed trick: a value roughly doubling or tripling each step signals multiplication. For series like 5, 10, 30, 120 the multipliers are 2, 3, 4. Memory aid: 'ratio rising' patterns usually use ×2, ×3, ×4… or ×1.5, ×2, ×2.5. When the multiplier is fractional, the series may rise then fall, so always confirm the ratio across at least two pairs before deciding.

IBPS Clerk frequently uses '×n then ±k' rules. Example: 2, 5, 11, 23, 47 follows ×2 +1 each time (2×2+1=5, 5×2+1=11). Another: 3, 7, 15, 31, 63 is ×2 +1. To detect, check if term = (previous × small number) ± constant. Speed method: pick a likely multiplier (usually 2 or 3), multiply the first term, and see what you must add to reach the second; then verify that same operation on the next pair. If it holds twice, apply it for the answer. These mixed series look intimidating but reduce to one repeated formula.

When a number sequence collapses from a giant first term down to a small one in only four or five steps, your brain is staring at a division series in disguise. The faster you recognise the signature, the fewer trial-and-error attempts you waste in the IBPS Clerk Prelims clock.

Definition: A number series is an ordered list of numbers that follow a hidden mathematical rule. Your job is to find that rule (multiply, divide, add, subtract, alternate operations, factorials, squares, etc.) and use it to identify the missing or wrong term.

Definition: A division-based descending series is one where each term is obtained by dividing the previous term — typically by an increasing sequence of integers (÷2, ÷3, ÷4, ÷5 …). It produces a fast collapse from a large opening number to a very small closing one.

The Tell-Tale Signature

The biggest clue a series is division-based is the shape of the collapse. Compare these two openings:

• 240, 232, 224, 216 — gentle, almost flat. This is arithmetic (subtracting 8).
• 480, 240, 80, 20 — steep, dropping by half, then a third, then a quarter. This is division.

Once your brain learns to feel "steep drop", you stop trying addition and subtraction first and jump straight to ratios.

Pattern 1 — Increasing Integer Divisor

Take the series 480, 240, 80, 20. Test the ratios between consecutive pairs:

• 480 ÷ 240 = 2
• 240 ÷ 80 = 3
• 80 ÷ 20 = 4

The divisors form a clean arithmetic progression: 2, 3, 4. The next divisor is 5, so the next term is 20 ÷ 5 = 4.

Always confirm the pattern across at least three consecutive divisions before locking it in — a single coincidence can mislead you.

Pattern 2 — Longer Division Chains

Sometimes the chain stretches across five terms: 720, 360, 120, 30, 6.

• 720 ÷ 360 = 2
• 360 ÷ 120 = 3
• 120 ÷ 30 = 4
• 30 ÷ 6 = 5

Same rule: divisors are 2, 3, 4, 5. If you were asked the next term, it would be 6 ÷ 6 = 1. If you were asked the wrong term, look for the position where the ratio breaks the pattern — that's the imposter.

Pattern 3 — Multiplication by a Fraction (×0.5, ×1/3 …)

Division by 2 is mathematically the same as multiplication by 0.5; division by 3 is the same as multiplication by 1/3. Some paper-setters disguise division series as fractional multiplication. The series 160, 80, 26.67, 6.67 might look strange until you realise it's ×1/2, ×1/3, ×1/4. Train your eye to spot fractional ratios as well as integer divisors.

Pattern 4 — Factorial Signposts

A subtler division-style family is the factorial series: 1, 2, 6, 24, 120. The ratios here are ×2, ×3, ×4, ×5 — going up, not down. But the giveaways are the numbers themselves: 24 (= 4!) and 120 (= 5!) are factorial landmarks every IBPS aspirant should memorise.

Useful factorials to know cold:

• 1! = 1
• 2! = 2
• 3! = 6
• 4! = 24
• 5! = 120
• 6! = 720

If you see any of these as a term — especially 6, 24, 120, 720 — pause and ask whether the series is factorial in either direction.

The Two-Way Mirror: Multiplication Up vs Division Down

The single most useful intuition in Number Series is this symmetry:

• A rising multiplier across an ascending sequence usually means multiply: 2, 6, 24, 120 (×3, ×4, ×5).
• A rising divisor across a descending sequence usually means divide: 480, 240, 80, 20 (÷2, ÷3, ÷4).

This is the same pattern, viewed from two ends. Once you internalise it, you stop solving "multiply" and "divide" series as separate categories — they are the same animal.

Question: Find the wrong number in the series 1440, 720, 240, 60, 15, 3.
Solution:
Step 1: Compute consecutive ratios.
Step 2: 1440 ÷ 720 = 2; 720 ÷ 240 = 3; 240 ÷ 60 = 4; 60 ÷ 15 = 4; 15 ÷ 3 = 5.
Step 3: The expected divisor chain is 2, 3, 4, 5, 6. The actual chain is 2, 3, 4, 4, 5 — the fourth division is off.
Conclusion: 15 is the wrong term. The correct value should have been 60 ÷ 5 = 12.

Why it matters: Number Series carries roughly 5 marks in IBPS Clerk Prelims, and division-style series appear in nearly every shift. The aspirants who clear sectional cut-offs are not necessarily the fastest — they are the ones who recognise the family of the series within the first three terms, without guessing.

Real-world example: When the Reserve Bank of India halves its repo rate at successive meetings to stimulate borrowing, the rate steps from, say, 6.5% to 3.25% to a fraction over time. Compounding effects in finance — depreciation of a vehicle, half-life of medication doses, declining EMI principal — all behave like descending division series in everyday Indian life.

Common misconception: Beginners often see a steep drop and write off the series as "random" or assume it must be subtraction with very large differences. They then waste 60 seconds testing −240, −160, −60 — three numbers that do not even form a pattern. The trained eye computes one ratio first, not one difference.

Cover the answer, recall, then check. 12 cards on multiplication and division based number series for IBPS Clerk Prelims.

Q1. How do you spot a multiplication/GP series?
A1. Divide each term by the previous one. A constant ratio (e.g. ×2, ×3) means it is a geometric/multiplication series.

Q2. Series: 3, 6, 12, 24, 48, ? Next term?
A2. 96. Constant ratio ×2 → 48 × 2 = 96.

Q3. Series: 5, 15, 45, 135, ? Next term?
A3. 405. Ratio ×3 → 135 × 3 = 405.

Q4. Series with a changing multiplier: 4, 8, 24, 96, 480, ? Next term?
A4. 2880. Multipliers are ×2, ×3, ×4, ×5, ×6 → 480 × 6 = 2880.

Q5. Series: 2, 6, 24, 120, ? Next term?
A5. 720. Multipliers ×3, ×4, ×5, ×6 → 120 × 6 = 720.

Q6. How do you recognise a division series?
A6. Terms fall and each divided into the previous gives a constant, e.g. ÷2 or ÷5.

Q7. Series: 1000, 200, 40, 8, ? Next term?
A7. 1.6. Constant ratio ÷5 → 8 ÷ 5 = 1.6.

Q8. Series: 4, 6, 9, 13.5, ? Which ratio, next term?
A8. 20.25. Ratio ×1.5 → 13.5 × 1.5 = 20.25.

Q9. Series: 7, 14, 42, 168, ? Next term?
A9. 840. Multipliers ×2, ×3, ×4, ×5 → 168 × 5 = 840.

Q10. Series: 640, 320, 160, 80, ? Next term?
A10. 40. Constant ÷2 → 80 ÷ 2 = 40.

Q11. Series with ×2 then +1 mixed: how to handle "×a ± b" patterns?
A11. Test a multiplier first; if the product misses by a fixed amount each step, add the constant (e.g. ×2 + 1).

Q12. Quickest way to tell multiplication from difference series?
A12. If terms grow much faster than a straight-line rise (roughly doubling/tripling), test ratios before differences.

Worked Example

Problem: Find the next term in the series: 5, 10, 30, 120, 600, ?

Solution:
Examine the ratio between consecutive terms.
10 ÷ 5 = 2
30 ÷ 10 = 3
120 ÷ 30 = 4
600 ÷ 120 = 5
Each term is multiplied by the next natural number: ×2, ×3, ×4, ×5. So the next multiplier is ×6.
Next term = 600 × 6 = 3600.

Answer: 3600