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Free Content10 MCQs
Imagine you are counting your steps while walking up a staircase: 1, 2, 3, 4, and so on. What comes next? You know it's 5! Number Series is just like finding these hidden rules in a line of numbers. It's super important for exams because it checks how well your brain can spot patterns and predict what comes next. Learning this helps you think smartly and quickly!
When you see a series, first quickly look at the gaps (differences) between the numbers. Write these gaps down. Most of the time, the pattern hides in these gaps! It could be simple addition, or the gaps themselves might follow a pattern.
If the numbers in a series are growing very fast, or look like common 'special' numbers, always check for squares or cubes. This is a very common trick used in exams. Quickly compare the numbers to 1, 4, 9, 16, 25... or 1, 8, 27, 64, 125...
Sometimes, a series has two different patterns hidden inside it. Don't just look at the next number. Try looking at every other number! This means, check the 1st, 3rd, 5th numbers as one series, and the 2nd, 4th, 6th numbers as another.
If numbers are increasing quite fast but not like perfect squares or cubes, think about multiplying and then adding/subtracting a small number. This pattern is very common. The multiplier (like ×2, ×3) and the number added/subtracted (+1, -2) often stay the same or also follow a simple pattern.
If a series has small, seemingly random numbers, quickly check if they are prime numbers (numbers only divisible by 1 and themselves, like 2, 3, 5, 7, 11...). This is a simple pattern to spot if you know your primes. They might be in order, or skipping one or two.
A Number Series is simply a sequence of numbers that follow a specific rule or pattern. Your job in competitive exams is to figure out that hidden rule. Once you know the rule, you can find the missing number or the wrong number in the series. It's like being a detective for numbers!
Let's look at the different kinds of patterns you might find:
Solving these questions needs a clear approach:
Arithmetic Series Rule
Next Term = Previous Term + Common Difference (d)Geometric Series Rule
Next Term = Previous Term × Common Ratio (r)Squares/Cubes Pattern
n², n³ or (n² ± k), (n³ ± k)Difference of Differences
Apply (Term₂ - Term₁), (Term₃ - Term₂), then (Difference₂ - Difference₁)| Series Type | How to Spot | Example Pattern |
|---|---|---|
| Arithmetic | Constant addition/subtraction | 2, 5, 8, 11, ? (+3) |
| Geometric | Constant multiplication/division | 4, 8, 16, 32, ? (×2) |
| Squares/Cubes | Numbers are n² or n³ or close to them | 1, 4, 9, 16, ? (n²) |
| Difference | Pattern in the differences between terms | 1, 2, 4, 7, 11, ? (+1, +2, +3, +4) |
| Mixed/Alternating | Two patterns running parallel or combined operations | 3, 6, 4, 8, 5, 10, ? (×2, -2, ×2, -3, ×2, -?) |
Q: Find the next number: 10, 12, 14, 16, ?
Q: What comes next in the series: 3, 9, 27, 81, ?
Q: Complete the series: 1, 4, 9, 16, 25, ?
Q: What is the missing number: 2, 3, 5, 8, 13, ?
In a game, your points double with each enemy defeated: 5, 10, 20, 40. If you defeat one more, what's your score?
Your older sibling promises to give you money like this: Day 1: ₹3, Day 2: ₹7, Day 3: ₹11, Day 4: ₹15. How much will you get on Day 5?
You stack apples in layers: 1 apple in the first layer, 4 in the second, 9 in the third, 16 in the fourth. How many apples will be in the fifth layer?
A new website gets visitors: 10 on day 1, 11 on day 2, 13 on day 3, 16 on day 4. How many visitors are expected on day 5?
Find the missing term: 1, 2, 6, 21, 88, ?
Which number is wrong in the series: 5, 11, 23, 47, 95, 190?
What is the next number: 7, 14, 28, 56, ?
Find the missing term: 100, 99, 95, 86, 70, ?
1What comes next in the sequence: 5, 10, 15, 20, ?
2Find the missing number: 2, 4, 8, 16, ?
3Complete the series: 1, 9, 25, 49, ?
4What is the next term: 6, 11, 17, 24, 32, ?
5Find the wrong number in the series: 10, 100, 1000, 10000, 1000000.
6What is the missing number: 1, 2, 4, 7, 11, ?
7Find the next number: 1, 8, 27, 64, ?
8What is the next number in the series: 3, 6, 12, 24, ?
9Find the missing term: 10, 9, 8, 7, 6, ?
10What comes next: 1, 4, 2, 8, 3, 12, ?
When you see a series, first quickly look at the gaps (differences) between the numbers. Write these gaps down. Most of the time, the pattern hides in these gaps! It could be simple addition, or the gaps themselves might follow a pattern.
If the numbers in a series are growing very fast, or look like common 'special' numbers, always check for squares or cubes. This is a very common trick used in exams. Quickly compare the numbers to 1, 4, 9, 16, 25... or 1, 8, 27, 64, 125...
Sometimes, a series has two different patterns hidden inside it. Don't just look at the next number. Try looking at every other number! This means, check the 1st, 3rd, 5th numbers as one series, and the 2nd, 4th, 6th numbers as another.
If numbers are increasing quite fast but not like perfect squares or cubes, think about multiplying and then adding/subtracting a small number. This pattern is very common. The multiplier (like ×2, ×3) and the number added/subtracted (+1, -2) often stay the same or also follow a simple pattern.
If a series has small, seemingly random numbers, quickly check if they are prime numbers (numbers only divisible by 1 and themselves, like 2, 3, 5, 7, 11...). This is a simple pattern to spot if you know your primes. They might be in order, or skipping one or two.
Next Term = Previous Term + Common Difference (d)Next Term = Previous Term × Common Ratio (r)n², n³ or (n² ± k), (n³ ± k)+1 more formulas below