Question

$200$ 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 the $200$ logs are placed and how many logs are in the top row

• A. $12$ rows, $8$ logs
• B. $114$ rows, $2$ logs
• C. $16$ rows, $4$ logs
• D. None of these
  

Answer 1

Answer: (D)

None of these

Given $a=20$ $d=-1$ $S_n=200$

$S_n=\frac{n}{2}[2a+(n-1)d]$

$200=\frac{n}{2}[40+(n-1)\times -1]$

$400=40n-n^2+n$

$n^2-41n+400=0$

$n^2-16n-25n+400=0$

$n(n-16)-25(n-16)=0$

$(n-16)(n-25)=0$

$n=16orn=25$

Since n can't be 25

$a_{25}=a+24d$

$=20-24=-4\left(notpossible\right)$

$n=16$

No. of logs in ${16}^{th}$ row are

$=20+(16-1)\times -1$

$=5$