Consider the following number pattern:$$12 = 3 \times 4$$$$20 = 4 \times 5$$$$30 = 5 \times 6$$\[42

Question

Consider the following number pattern:$$12 = 3 \times 4$$$$20 = 4 \times 5$$$$30 = 5 \times 6$$$$42 = 6 \times 7$$$$\dots$$$$342 = (t + 2)(t + 3)$$$$\dots$$ Write down the $5^{th}$ and the $6^{th}$ row of the number pattern. By finding the integer value of $t$, determine which row does $342$ appear. Find a formula for the $n^{th}$ row of the pattern in terms of $n$.

Accepted Answer

(i) $56=7\times8$ and $72=8\times9$ (ii) $t=16$, so the 16th row (iii) $T_n=(n+2)(n+3)$

Number Patterns

Number Patterns

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