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

Question

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?

Accepted Answer

Step 1: Let the number of rows be $n$.
A.P. formed is $22, 21, 20, 19, \ldots$
Here $a = 22$, $d = -1$, $S_n = 250$
Step 2: $	herefore 250 = \frac{n}{2}[44 + (n-1)(-1)]$
$\Rightarrow n^2 - 45n + 500 = 0$
Step 3: $\Rightarrow (n - 25)(n - 20) = 0$
$n = 25$ $	herefore n = 20$
Step 4: Logs in top row $= a_{20} = 22 + 19(-1) = 3$

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