This image is a "Fact sheet" on "Triangular numbers" for Year 3 Numeracy. The task is to understand the pattern of triangular numbers and likely to continue it or find the next number in the sequence.
Here is the solution and explanation:
The image displays the first nine triangular numbers, visually represented as dots arranged in equilateral triangles.
The Pattern:
A triangular number is the sum of the first `n` natural numbers (1, 2, 3, 4, ...).
- The
1st triangular number is 1.
- The
2nd triangular number is 1 + 2 = 3.
- The
3rd triangular number is 1 + 2 + 3 = 6.
- The
4th triangular number is 1 + 2 + 3 + 4 = 10.
- And so on...
The general formula for the `n`th triangular number is:
T(n) = n × (n + 1) / 2
The Sequence Shown:
The image lists the following triangular numbers:
- T(1) = 1
- T(2) = 3
- T(3) = 6
- T(4) = 10
- T(5) = 15
- T(6) = 21
- T(7) = 28
- T(8) = 36
- T(9) = 45
Finding the Next Triangular Number (T(10)):
To find the 10th triangular number, we add the next natural number, which is 10, to the previous sum (which was 45 for T(9)).
T(10) = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
T(10) = 45 + 10
T(10) =
55
Alternatively, using the formula:
T(10) = 10 × (10 + 1) / 2
T(10) = 10 × 11 / 2
T(10) = 110 / 2
T(10) =
55
Therefore, the next triangular number after 45 is
55.
Parent Tip: Review the logic above to help your child master the concept of triangular numbers worksheet.
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