# Number Series Questions with Answers — Find the Missing Term

> Number and alphabet series questions with answers. Learn to spot differences, ratios, squares and alternating patterns, with solved examples.

Source: https://www.sansal.in/aptitude/series · Last updated: 2026-09-19 · How often it appears: Very high. Present in essentially every aptitude paper.

Series questions are a search problem: you are looking for the rule, and there is a fixed order worth searching in. Checking differences first, then ratios, then squares and cubes, then alternating patterns will find the rule in the large majority of questions.

## Concepts

### Search in a fixed order

Take consecutive differences first. If those are constant you have an arithmetic series; if the differences themselves form a pattern, that is a second-order series. Only if differences fail should you try ratios, then squares and cubes, then alternating or interleaved sequences. Searching in a set order is much faster than staring.

### Recognise the standard sequences on sight

Squares 1, 4, 9, 16, 25; cubes 1, 8, 27, 64, 125; primes 2, 3, 5, 7, 11; Fibonacci-style where each term is the sum of the previous two. A term like 121 or 169 should immediately suggest squares.

### Two series can be interleaved

If nothing works on consecutive terms, check the odd-numbered and even-numbered positions as two separate series. Alternating series are common precisely because they defeat the usual difference check.

### Alphabet series use positions

Convert letters to their positions and the problem becomes a number series. Do not try to see the pattern in the letters themselves.

## Formulas

| Formula | Rule | Note |
| --- | --- | --- |
| Arithmetic series | Each term = previous + d (constant difference) |  |
| Geometric series | Each term = previous × r (constant ratio) |  |
| Second-order | The differences themselves form a pattern |  |
| Fibonacci style | Each term = sum of the two before it |  |
| Squares | 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169 |  |
| Cubes | 1, 8, 27, 64, 125, 216, 343 |  |

## Worked examples

### Example 1

**Question:** Find the next term: 2, 6, 12, 20, 30, ?

**Solution:**

1. Take differences: 6−2=4, 12−6=6, 20−12=8, 30−20=10
2. The differences are 4, 6, 8, 10 — increasing by 2 each time, so the next difference is 12.
3. Next term = 30 + 12

**Answer:** 42

**Check:** These are also n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7 = 42. Two routes, same answer.

### Example 2

**Question:** Find the next term: 3, 6, 12, 24, ?

**Solution:**

1. Differences are 3, 6, 12 — not constant, and they double, which hints at a ratio.
2. Check ratios: 6/3 = 2, 12/6 = 2, 24/12 = 2. Constant ratio of 2.
3. Next = 24 × 2

**Answer:** 48

### Example 3

**Question:** Find the missing term: 1, 4, 9, 16, 25, ?

**Solution:**

1. Differences are 3, 5, 7, 9 — odd numbers increasing by 2, which is the signature of squares.
2. Indeed the terms are 1², 2², 3², 4², 5².
3. The next term is 6².

**Answer:** 36

## Practice questions

1. Find the next term: 5, 10, 20, 40, ?
   - A. 60
   - B. 70
   - C. 80
   - D. 100
   - **Answer:** C. 80 — Each term doubles. 40 × 2 = 80.

2. Find the next term: 2, 5, 10, 17, 26, ?
   - A. 35
   - B. 37
   - C. 39
   - D. 41
   - **Answer:** B. 37 — Differences are 3, 5, 7, 9, so the next is 11. 26 + 11 = 37. (The terms are n² + 1.)

3. Find the next term: 1, 1, 2, 3, 5, 8, ?
   - A. 11
   - B. 12
   - C. 13
   - D. 15
   - **Answer:** C. 13 — Fibonacci — each term is the sum of the two before it. 5 + 8 = 13.

4. Find the next term: 1, 8, 27, 64, ?
   - A. 100
   - B. 115
   - C. 125
   - D. 144
   - **Answer:** C. 125 — These are cubes: 1³, 2³, 3³, 4³. Next is 5³ = 125.

5. Find the next letter: A, C, E, G, ?
   - A. H
   - B. I
   - C. J
   - D. K
   - **Answer:** B. I — Positions 1, 3, 5, 7 — increasing by 2. Next is position 9, which is I.

6. Find the odd one out: 4, 9, 16, 24, 36
   - A. 9
   - B. 16
   - C. 24
   - D. 36
   - **Answer:** C. 24 — All are perfect squares (2², 3², 4², 6²) except 24.

7. Find the next term: 100, 81, 64, 49, ?
   - A. 30
   - B. 32
   - C. 36
   - D. 40
   - **Answer:** C. 36 — Descending squares: 10², 9², 8², 7². Next is 6² = 36.

## Where marks get lost

- Giving up after the difference check instead of moving on to ratios and squares.
- Missing an interleaved series because only consecutive terms were compared.
- Trying to read alphabet patterns as letters instead of converting to positions.
- Finding a rule that fits the first two terms and not testing it against the rest.

## Related topics

- [Coding–Decoding](https://www.sansal.in/aptitude/coding-decoding)
- [Number System](https://www.sansal.in/aptitude/number-system)
- [Syllogism](https://www.sansal.in/aptitude/syllogism)

Practise these on Sansal: https://www.sansal.in/practice/aptitude