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200 logs are stacked in the following manner , 20 logs in the bottom row, 19 in the next row , 18 in the next to it and so on , In how may rows are the 200 logs placed and how many logs are in the top now ? |
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Answer» re total 200 logs.20 logs in bottom ROW , 19 in the NEXT row , 18 in the next and do on.Total number of rows in which 200 logs are placed.Number of logs present in top row.Total number of logs is 200.We know , s(N) = 200a = 20d = 19-20 = -1Putting values , we get , HENCE , number of rows are 16 or 25.______________________________________We will find number of logs in both case.ㅤㅤㅤㅤㅤㅤㅤㅤ★ a(n) = a + (n-1)dㅤㅤㅤㅤㅤㅤㅤㅤFor n = 16 , ㅤㅤㅤㅤㅤㅤㅤㅤ→ a(16) = a + 15dㅤㅤㅤㅤㅤㅤㅤㅤ→ a(16) = 20 + 15(-1)ㅤㅤㅤㅤㅤㅤㅤㅤ→ a(16) = 20-15ㅤㅤㅤㅤㅤㅤㅤㅤ→ a(16) = 5__________________________________________For n = 25 , ㅤㅤㅤㅤㅤㅤㅤㅤ→ a(25) = a + (24d)ㅤㅤㅤㅤㅤㅤㅤㅤ→ a(25) = 20 + 24(-1)ㅤㅤㅤㅤㅤㅤㅤㅤ→ a(25) = 20-24ㅤㅤㅤㅤㅤㅤㅤㅤ→ a(25) = -4ㅤㅤㅤㅤㅤㅤㅤㅤNegative value is not possible .ㅤㅤㅤㅤㅤㅤㅤㅤHence , Total number of rows is 16 and number of logs in top row is 5. |
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