Let’s solve each question one by one.
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Question 1: What is the formula used to find a triangular number?
Triangular numbers are numbers that can form an equilateral triangle. The first few are:
- 1st: 1
- 2nd: 3 (1 + 2)
- 3rd: 6 (1 + 2 + 3)
- 4th: 10 (1 + 2 + 3 + 4)
The pattern is: add all whole numbers from 1 up to n.
There’s a shortcut formula for this sum:
T = n(n + 1) / 2
Let’s check the options:
- 2T = (n)(n + 1) / 2 → This would mean T = n(n+1)/4 — wrong.
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T = (n)(n + 1) / 2 → Correct!
- T = (n)(n + 1) → Too big — misses the division by 2.
- T = (n)(n - 1) / 2 → That’s for something else (like combinations).
✔ So, correct answer:
T = (n)(n + 1) / 2
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Question 2: What does n represent in finding triangular numbers?
In the formula T = n(n + 1)/2, “n” tells us which triangular number we’re finding.
For example:
- If n = 1 → T = 1 → 1st triangular number
- If n = 2 → T = 3 → 2nd triangular number
- If n = 3 → T = 6 → 3rd triangular number
So, “n” is the position or term number in the sequence.
Check options:
- The term in the sequence → Vague — could mean the value, not the position.
- The number of dots in each triangle → No, that’s T, the result.
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The number of terms in the sequence → YES! Because if you want the 5th triangular number, you add 1+2+3+4+5 → 5 terms.
- The height of the equilateral triangle → Not really — it’s more about rows of dots.
✔ So, correct answer:
The number of terms in the sequence.
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Question 3: What is the 12th triangular term?
Use the formula: T = n(n + 1)/2
Plug in n = 12:
T = 12 × 13 / 2
= 156 / 2
=
78
Check options:
- T = 156 → That’s 12×13, forgot to divide by 2.
- T = 66 → That’s 11×12/2 → 11th term.
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T = 78 → Correct!
- T = 39 → Half of 78 — maybe divided twice?
✔ So, correct answer:
T = 78
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Final Answer:
1. T = (n)(n + 1) / 2
2. The number of terms in the sequence.
3. T = 78
Parent Tip: Review the logic above to help your child master the concept of triangular numbers worksheet.
