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250 logs are stacked in the following manner:
22 logs in the bottom row, 21 in the next row, 20 in the row next to it and so on (as shown by an example). In how many rows, are the 250 logs placed and how many logs are there in the top row?
22 logs in the bottom row, 21 in the next row, 20 in the row next to it and so on (as shown by an example). In how many rows, are the 250 logs placed and how many logs are there in the top row?
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Here $a = 22, d = – 1$ $S_n = 250$
$\therefore 250 = \frac{n}{2} [44 + (n – 1) (-1)]$
$\Rightarrow n^2 - 45n + 500 = 0$
$\Rightarrow (n-25) (n – 20) = 0$
$n\neq 25 \therefore n = 20$
logs in top row = $a_{20} = 22 + 19 (- 1) = 3$
$\therefore 250 = \frac{n}{2} [44 + (n – 1) (-1)]$
$\Rightarrow n^2 - 45n + 500 = 0$
$\Rightarrow (n-25) (n – 20) = 0$
$n\neq 25 \therefore n = 20$
logs in top row = $a_{20} = 22 + 19 (- 1) = 3$