Patterns

Answer

Step 1: Use the formula for triangular numbers: $X_n = \frac{n(n+1)}{2}$ Step 2: Plug in $n = 5$: $$ X_5 = \frac{5(5+1)}{2} = \frac{5 \times 6}{2} = \frac{30}{2} = 15 $$ Answer: 15…

Answer

Step 1: Square numbers are formed by $n \times n$ Step 2: For $n = 7$: $$ 7 \times 7 = 49 $$ Answer: 49…

Answer

Step 1: Use the triangular number formula: $X_n = \frac{n(n+1)}{2}$ Step 2: Try values of $n$: - $n = 6$: $\frac{6 \times 7}{2} = 21$ ✅ Yes, 21 is the 6th triangular number. Answer: Yes…

Answer

Step 1: Observe the pattern — each number increases by 5. Step 2: $20 + 5 = 25$ Answer: 25…

Answer

Step 1: Difference between terms: $60 - 48 = 12$, $72 - 60 = 12$, so rule is +12 Step 2: Subtract 12 from 48: $48 - 12 = 36$ Step 3: Subtract 12 from 36: $36 - 12 = 24$ Answer: 24, 36, 48, 60, 72, …

Answer

Step 1: Use $n \times n$ where $n = 10$ $$ 10 \times 10 = 100 $$ Answer: 100…

Answer

Step 1: Check if 36 can be written as $n \times n$ Step 2: $6 \times 6 = 36$ ✅ Yes, 36 is the 6th square number. Answer: Yes…

Answer

Step 1: Use formula $X_n = \frac{n(n+1)}{2}$ Step 2: $n = 8$ $$ X_8 = \frac{8 \times 9}{2} = \frac{72}{2} = 36 $$ Answer: 36…