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Number Series 4

Number Series 4 explores triangular numbers. Pupils practise spotting these special sequences, which connect maths and visual patterns, in 11 Plus Verbal Reasoning questions.

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Fascinating Fact:

Triangular numbers, like 1, 3, 6, 10, form perfect triangle shapes when drawn with dots.

In 11 Plus Verbal Reasoning, number sequences include triangular, square, and cube numbers. Recognising these helps students solve puzzles quickly and apply mathematical thinking to reasoning problems.

Key Terms

Triangular Number: A number that can form a triangle pattern, such as 3, 6, or 10.
Sequence: A list of numbers ordered by a rule or pattern.
Reasoning: The process of thinking logically to solve a problem or puzzle.

Learn more with our guide to 11 Plus courses and materials.

Frequently Asked Questions (Click to see answers)

What is a triangular number?

A triangular number is a number that can be arranged into a triangle, like 1, 3, 6, or 10.

How do you find triangular numbers?

Triangular numbers are found by adding consecutive numbers: 1, then 1+2=3, then 1+2+3=6, and so on.

Why do triangular numbers matter in the 11 Plus?

Triangular numbers are important because they appear in number sequence puzzles and test logical thinking in Verbal Reasoning.

Try These Related Quizzes

Example: What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.

2 4 6 8 10 (?)

12
11
14
2

The correct answer is 12 because the numbers are going up by 2 each time. 10 + 2 = 12.

1 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
835, 724, 613, 502, (?)

319

764

456

391

The correct answer is 391 because the numbers are going down by 111 each time. 502 - 111 = 391. 111 is a certain kind of number, and shares its name with the words noon, mum and poop. Do you know its name? Read further down to find out

2 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
490, 369, 248, 127, (?)

The correct answer is 6 because the numbers are going down by 121 each time. There really is no way around working this one out with a pencil! 127 - 121 = 6

3 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
81, 9, 72, 8, (?)

The correct answer is 63 because the numbers are all part of the 9 times tables. 81 divided by 9 = 9, 72 divided by 9 = 8, so we are looking for what divided by 9 = 7? The answer is 63

4 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
84, 840, 8400, 84000, (?)

8410

84000000

840000

8400000

The correct answer is 840000 because the numbers are multiplied by 10 each time. Remember the easy rule for multiplying a number by 10? Just add a nought (0)

5 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
6, 36, 216, 1296, 7776, (?)

46656

45656

44656

47656

The correct answer is 46656 because the numbers are multiplied by 6 each time. Did you know that the number six in French is spelt six, while in Russian it is ????? (pronounced shest.) The puzzle in question 1 asked about 111, poop, mum and noon. They are all palindromes. Well done if you got it right!

6 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
123, 100, 77, 54, (?)

The correct answer is 31 because the numbers are going down by 23 each time. 23 is a prime number made up from two other prime numbers (2 and 3)

7 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
32, 44, 56, 68, (?)

The correct answer is 80 because the numbers are going up by 12 each time. 68 + 12 = 80

8 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
89, 78, 67, 56, (?)

The correct answer is 45 because the numbers are going down by 11 each time. 56 - 11 = 45

9 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
776, 665, 554, 443, (?)

334

332

321

345

The correct answer is 332 because the numbers are going down each time by 111 so we are looking for 443 - 111 = 332. You may have figured out that we like the number 111. We have used it a few times in this series of quizzes because it is such an interesting number! A palindrome (reading the same backwards and forwards), it is also a number which can be divided equally by two prime numbers (37 and 3). But we really like the fact that it is sometimes referred to as a 'Nelson'. Admiral Nelson had 'One Eye, One Arm, One Leg!'

10 .

What is the next number in the series of numbers below? Replace the question mark with a number and select the correct answer from the four choices available.
810, 270, 90, 30, (?)

The correct answer is 10 because the numbers are being divided by 3 each time. So we are looking for 30 divided by 3 = 10. Wow! You have completed the fourth and final Number Series quiz. We hope you enjoyed these (and the little puzzles and facts that were hidden in the answers). Why not look at some of our other Verbal Reasoning quizzes?

Author: Stephen O'Hara