Why this topic matters · 7 min read
Number Series is one of the most scoring topics in SSC MTS Reasoning. You can expect 2 to 4 questions per paper. Questions ask you to find the missing number or the wrong number in a sequence. The series follow simple patterns like addition, subtraction, multiplication, squares, cubes, or a mix. Since SSC MTS is a 10th-pass level exam, patterns are not too complex. Spotting the pattern quickly is the real skill here.
Addition and Subtraction Series
In these series, a fixed number or an increasing number is added or subtracted each time. This is the most basic type and appears very often. Sometimes the difference itself increases by a fixed amount, which is called a difference-of-difference pattern.
- Fixed addition: 3, 7, 11, 15, 19 — adding 4 each time
- Fixed subtraction: 50, 44, 38, 32 — subtracting 6 each time
- Increasing difference: 2, 3, 5, 8, 12 — differences are 1, 2, 3, 4
- Decreasing difference: 20, 17, 15, 14 — differences are 3, 2, 1
- Always check differences between consecutive terms first — it is the fastest trick
Key formulas
nth Term (fixed addition)
T(n) = First Term + (n-1) x Common Difference
When: When each step adds the same number
Worked examples
Series: 4, 9, 14, 19, ?, 29. Differences: all 5. Missing = 19 + 5 = 24.
Series: 1, 2, 4, 7, 11, ?. Differences: 1, 2, 3, 4, so next difference = 5. Answer = 11 + 5 = 16.
Multiplication and Division Series
Here each term is multiplied or divided by a fixed number to get the next term. These are called geometric-style series. Sometimes the multiplier alternates between two numbers. SSC MTS keeps the multiplier simple — usually 2, 3, or 0.5.
- Fixed multiply: 2, 6, 18, 54 — multiply by 3 each time
- Fixed divide: 256, 64, 16, 4 — divide by 4 each time
- Alternating multiply: 2, 4, 12, 24, 72 — multiply alternately by 2 and 3
- If numbers grow very fast, think multiplication first
- If numbers shrink rapidly or are fractions, think division
Key formulas
Geometric Term
T(n) = First Term x r^(n-1)
When: When each term is multiplied by same ratio r
Worked examples
Series: 3, 6, 12, 24, ?. Each term x2. Answer = 48.
Series: 5, 10, 30, 60, 180, ?. Pattern: x2, x3, x2, x3, x2. Answer = 360.
Squares and Cubes Series
These series are based on perfect squares (1, 4, 9, 16, 25...) or perfect cubes (1, 8, 27, 64, 125...) or a mix. Sometimes a number is added or subtracted from the square or cube. Memorize squares up to 20 and cubes up to 10 — it saves 30 seconds per question.
- Pure squares: 1, 4, 9, 16, 25, 36 — squares of 1, 2, 3, 4...
- Pure cubes: 1, 8, 27, 64, 125
- Squares plus constant: 2, 5, 10, 17, 26 — squares of 1,2,3,4,5 plus 1
- Mixed: 1, 8, 27, 64 then 25, 36... — alternating squares and cubes
- Tip: if you see 4, 9, 16 or 8, 27, 64 — immediately think squares or cubes
Key formulas
Squares to remember
1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400
When: Identify square-based series instantly
Cubes to remember
1,8,27,64,125,216,343,512,729,1000
When: Identify cube-based series instantly
Worked examples
Series: 1, 4, 9, 16, ?, 36. Squares of 1 to 6. Missing = 25.
Series: 2, 9, 28, 65, ?. Pattern: 1^3+1, 2^3+1, 3^3+1, 4^3+1. Answer = 5^3+1 = 126.
Two-Step and Mixed Pattern Series
These series combine two operations. For example, multiply then add, or add then square. SSC MTS occasionally puts one such question to test sharper candidates. The key is to look at pairs of operations rather than just one step at a time.
- Multiply then add: 1, 3, 7, 15, 31 — each term = previous x2 + 1
- Add then multiply: 2, 5, 11, 23 — each term = previous x2 + 1
- Prime number series: 2, 3, 5, 7, 11, 13 — all primes in order
- Fibonacci-style: 1, 1, 2, 3, 5, 8, 13 — each = sum of previous two
- If no single operation works, try two-step: do something to get next term
Worked examples
Series: 1, 3, 7, 15, 31, ?. Each term = previous x2 + 1. Answer = 31 x2 + 1 = 63.
Series: 2, 3, 5, 7, 11, ?. All prime numbers. Next prime = 13.
Wrong Number in Series
Some SSC MTS questions give a complete series but one number does not fit the pattern. You have to find the odd one out. The approach is the same — find the pattern using most of the terms, then check which term breaks it.
- Find the rule using at least 3-4 terms first
- Then test each term — the one that breaks the rule is wrong
- Wrong number questions appear less often in MTS but do appear
- Do not change more than one number — only one is wrong
- Cross-check by seeing if removing that number makes the rest perfect
Worked example
Series: 2, 4, 8, 16, 35, 64. Pattern is x2 each time. 35 should be 32 (16x2). Wrong number = 35.
⚠ Common mistakes to avoid
- Checking only addition first and giving up if it does not work — always try multiplication too before moving on
- Forgetting that the difference itself can follow a pattern — missing increasing or decreasing difference series
- Confusing squares and cubes — 64 is both 8 squared and 4 cubed, so check both possibilities
- In wrong number questions, changing two numbers — only one number is wrong, stick to finding just one
- Wasting time on a complex-looking series — in SSC MTS the pattern is always simple, look again with fresh eyes
🧠 Memory aids
- AMSD rule: Always check Addition first, then Multiplication, then Squares, then Doubles+1 — follow this order every time
- Think of the series as steps on a staircase — are the steps equal (fixed addition) or getting bigger (increasing difference) or doubling (multiplication)?
- Squares rap: 1,4,9,16 — one four nine sixteen — chant it like a rhyme until it sticks
- For two-step series, whisper x2+1 or x2-1 — these two patterns cover 80 percent of mixed series in SSC MTS
🎯 SSC MTS exam tips
- SSC MTS typically asks 2 to 3 series questions — all are straightforward, no tricky multi-pattern series like SSC CGL
- Time target is 30 to 40 seconds per series question — if you are taking more than a minute, skip and return
- Missing number questions are more common than wrong number questions in recent MTS papers
- Differences between consecutive terms is the first thing to write on rough paper — it solves 60 percent of questions instantly
- If the series has large numbers like 256, 512, 1024 — it is almost always a powers-of-2 or powers-of-3 series, do not overthink it
Q1 · medium · PYQ 2022
In the following question, select the missing number of the given series.
34, 365, 388, ?, 434, 457
- 430
- 425
- 411
- 435
Q2 · hard · AI-verified
In the following number series, identify the missing term: 7, 14, 42, 168, 840, ?
- 5040
- 4320
- 3360
- 6720
Q3 · medium · PYQ 2025
Select the option that will come in place of the question mark (?) in the following series: 203, –206, –209, –212, –215, –218, –221, –224, ?
- –225
- –227
- –226
- –228
Q4 · medium · PYQ 2014
Find the missing number in the series: 7, 14, 23, 34, ?
- 45
- 51
- 49
- 47
Q5 · medium · PYQ 2020
Which number will replace the question mark (?) in the following number series? 9, 12, 17, 26, 43, 76, ?, 270
- 141
- 133
- 154
- 125