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Observe the following pattern in which each small square represents a unit square (square of side $1$ unit).
nIf the sum of number of unit squares in the $n^{th}$ figure and $(n + 2)^{th}$ figure is $290$, find the value of $n$.
nIf the sum of number of unit squares in the $n^{th}$ figure and $(n + 2)^{th}$ figure is $290$, find the value of $n$.
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Number of unit squares in the $n^{th}$ figure = $n^2$ (1/2 Mark)
nNumber of unit squares in the $(n + 2)^{th}$ figure = $(n + 2)^2$ (1/2 Mark)
n$n^2 + (n + 2)^2 = 290$ (1 Mark)
n$n^2 + n^2 + 4n + 4 = 290$
n$2n^2 + 4n - 286 = 0$
n$n^2 + 2n - 143 = 0$ (1 Mark)
n$(n + 13)(n - 11) = 0$ (1 Mark)
n$n = 11$, $n = -13$ (rejected) (1 Mark)
nNumber of unit squares in the $(n + 2)^{th}$ figure = $(n + 2)^2$ (1/2 Mark)
n$n^2 + (n + 2)^2 = 290$ (1 Mark)
n$n^2 + n^2 + 4n + 4 = 290$
n$2n^2 + 4n - 286 = 0$
n$n^2 + 2n - 143 = 0$ (1 Mark)
n$(n + 13)(n - 11) = 0$ (1 Mark)
n$n = 11$, $n = -13$ (rejected) (1 Mark)