Consider the following number pattern: $ 1 = 1 = 1^2$ $ 1 + 3 = 4 = 2^2$ \( 1 + 3 + 5 = 9 = 3^2\

Question

Consider the following number pattern: $ 1 = 1 = 1^2$ $ 1 + 3 = 4 = 2^2$ $ 1 + 3 + 5 = 9 = 3^2$ $ 1 + 3 + 5 + 7 = 16 = 4^2$ $...$ $ 1 + 3 + 5 + ... + k = 289 =$ $...$ Write down the $5^{th}$ and the $6^{th}$ row of the number pattern. Fill in the blank in the row containing $k$ and find the value of $k$. Find a formula for the ${n^{\mathrm{th}}}$ row of the pattern in terms of ${n}$ .

Accepted Answer

(i) $25=5^2$ and $36=6^2$ (ii) $17^2$, $k=33$ (iii) $1+3+5+\cdots+(2n-1)=n^2$

Number Patterns

Number Patterns

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