Roof

Tiles are stacked in rows on the trapezoidal shaped roof.
At the ridge is 15 tiles and each subsequent row has one more tile than in the previous row.

How many tiled is covered roof if lowermost row has 37 tiles?

Result

x =  598

Solution:

$a_1 = 15 \ \\ a_n = 37 \ \\ d = 1 \ \\ \ \\ a_n = a_1 + (n-1)d \ \\ n = 37-15+1 = 23 \ \\ \ \\ x = \dfrac{n}{2}(a_1+a_n) = \dfrac{ 23}{2}(15+37) = 598$

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