Roof

Tiles are stacked in rows on the trapezoidal-shaped roof. At the ridge are 47 tiles, and each subsequent row has one more tile than the previous row.

How many tiles are covered the roof if the lowermost row has 69 tiles?

Correct answer:

x =  1334

Step-by-step explanation:

a1=47 an=69 d=1  an = a1 + (n1)d n=ana1+1=6947+1=23  x=n2 (a1+an)=232 (47+69)=1334a_{1} = 47 \ \\ a_n = 69 \ \\ d = 1 \ \\ \ \\ a_n\ = \ a_{1}\ +\ (n-1)d \ \\ n = a_n-a_{1}+1 = 69-47+1 = 23 \ \\ \ \\ x = \dfrac{ n }{ 2 } \cdot \ (a_{1}+a_n) = \dfrac{ 23 }{ 2 } \cdot \ (47+69) = 1334



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