# Arithmetic Progressions

#### Question 19:

200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?

#### Answer:

It can be observed that the numbers of logs in rows are in an A.P.

20, 19, 18…

For this A.P.,

*a* = 20

*d* = *a*_{2}
− *a*_{1} = 19 − 20 = −1

Let a total of 200 logs
be placed in *n* rows.

*S*_{n}
= 200

400 = *n* (40 −
*n* + 1)

400 = *n *(41 −
*n*)

400 = 41*n* −
*n*^{2}

*n*^{2} −
41*n *+ 400...

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