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Which number is the Land Rover parked on?

puzzle[1]

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My answer is

$59$

The sequence advances by the next natural square

Sequence:
$5$ $9$ $18$ $34$ $59$ $95$

Differences:
$4$ $9$ $16$ $25$ $36$

And the next term will be $144$ which is $95 + 49$

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The parking spots fit the sequence A153058.

$a(0)=4; \hspace{1em} a(n)=n^2+a(n-1)$

i.e. Starting from the number 4, add the square of the parking space's index to the previous parking space's number.

$a(1) = 5$
$a(2) = 9$
$a(3) = 18$
$a(4) = 34$
$a(5) = 59$
$a(6) = 95$

The $n^{\text{th}}$ parking space (for $n \geq 0$) can be found using the solved recurrence:

$\begin{gather*}a(n) = 4 + \frac{n (1 + n) (1 + 2 n)}{6}\end{gather*}$

Therefore, the missing number, on the fifth parking space, is $59$.


(This is the same answer as @WeatherVane's.)

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