SEAGReady
NumberP7 level18 questions in the full course

Triangular NumbersSEAG Practice Questions

Understanding triangular numbers as sums of consecutive integers (1, 3, 6, 10, 15...) and recognising the pattern.

Where your child meets this in real life: Recognising and continuing number patterns, understanding sequential sums

What your child needs to know

SEAGReady breaks triangular numbers into 2 steps, taught in order so each skill builds on the last.

  1. 1

    Recognise the Pattern

    Identify and continue the triangular number sequence by recognising the increasing differences

  2. 2

    Generate from Sums

    Calculate triangular numbers using cumulative sums of consecutive integers starting from 1

Try these SEAG-style questions

Three free sample questions from our triangular numbers course. Every question comes with a full explanation, and hints that guide without giving the answer away.

Question 1Confidence builder

Daniel's first five triangular orange arrangements contain 1, 3, 6, 10 and 15 oranges. How many oranges will the next arrangement contain?

Answer choices for question 1
Question 2Confidence builder

What is 1 + 2 + 3 + 4 + 5? (This is the 5th triangular number)

Answer choices for question 2
Question 3Confidence builder

Erin knows that 1 + 2 + 3 + 4 = 10. She wants to find 1 + 2 + 3 + 4 + 5. What should she add to 10?

Answer choices for question 3

Try the lesson: Recognise the Pattern

This is the exact interactive worked example your child sees in SEAGReady. Step through it and watch the method build up.

Amara is arranging cans in a pyramid display. Each row has one more can than the row above. The rows have 1, 3, 6, 10, 15 cans so far.

How many cans will the next row have?

1, 3, 6, 10, 15, ?

Find the differences between terms
1

Look at the gap between each pair

Step 1 of 4

Prefer to read? See every step written out

Amara is arranging cans in a pyramid display. Each row has one more can than the row above. The rows have 1, 3, 6, 10, 15 cans so far.

How many cans will the next row have?

  1. 1

    Find the differences between terms

    • Look at the gap between each pair
    • Differences are: +2, +3, +4, +5...3−1=2, 6−3=3, 10−6=4, 15−10=5
  2. 2

    Spot the pattern in the differences

    • The differences go up by 1 each time
    • Next difference will be +615 + 6 = 21

The next row will have 21 cans.

The key insight: The jumps grow by 1 each time: +2, +3, +4, +5, +6...

Common mix-up: Adding 5 again to get 20. The difference increases each time - it's not constant like in times tables.

Mistakes to watch for

These are the misconceptions we see most often in triangular numbers, including the ones our practice questions are specifically designed to catch.

  • Confusing with triangle angles or properties
  • Not seeing the pattern (add 2, add 3, add 4...)
  • Difficulty generating the next term

Build these skills first

Struggling with triangular numbers? The real gap is often in one of these earlier topics.

Number Sequences

More number practice

Read & Write Whole NumbersIdentify Place Value of a DigitCompare Two Whole NumbersOrder a Set of Whole NumbersAddition Facts to 20Subtraction Facts Within 20
18 questions on this topic alone

Master triangular numbers and everything it unlocks

SEAGReady finds the exact step where your child gets stuck, teaches it with worked examples like the one above, and brings it back for review so it sticks.

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