Consider the following number pattern: $$1^2 - 0^2 = 1$$ $$2^2 - 1^2 = 3$$ $$3^2 - 2^2 = 5$$ \[\dots

Question

Consider the following number pattern: $$1^2 - 0^2 = 1$$ $$2^2 - 1^2 = 3$$ $$3^2 - 2^2 = 5$$ $$\dots$$ $$m^2 - (m - 1)^2 = 65$$ $$\dots$$ Write down the $5^{th}$ and the $6^{th}$ row of the number pattern. Write down, in terms of $n$, the equation that appears in the $n^{th}$ row of the pattern. Find the integer value of $m$.

Accepted Answer

(i) $5^2-4^2=9$ and $6^2-5^2=11$ (ii) $n^2-(n-1)^2=2n-1$ (iii) $m=33$

Number Patterns

Number Patterns

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