Our top 5% students will be awarded a special scholarship to Lido.

Ncert solutions

CHAPTERS

**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. How many logs are in the top row?**

We can see that the numbers of logs in rows are in the form of an A.P.20, 19, 18…

For the given A.P.,

*First term, a* = 20 and common difference, _d_ = _a_2−_a_1 = 19−20 = −1

Let a total of 200 logs be placed in _n_ rows.

*Thus, Sn* = 200

By the sum of nth term formula,

\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d}] \\ 200=\frac{\mathrm{n}}{2}(2(20)+(\mathrm{n}-1)(-1)) \\ 400=n(40-n+1) \\ 400=n(41-n) \\ 400=41 n-n 2 \\ n^{2}-41 n+400=0 \\ n^{2}-16 n-25 n+400=0 \\ n(n-16)-25(n-16)=0 \\ (n-16)(n-25)=0 \\ \text { Either }(n-16)=0 \text { or } n-25=0 \\ n=16 \text { or } n=25

By the nth term formula,

*a _{n}* =

*a*_{16} = 20+(16−1)(−1)

*a*_{16} = 20−15

*a*_{16} = 5

Similarly, the 25^{th} term could be written as;

*a*_{25} = 20+(25−1)(−1)

*a*_{25} = 20−24

*a*_{25} = –4

It can be seen, the number of logs in 16^{th} row is 5 as the numbers cannot be negative.

Therefore, 200 logs can be placed in 16 rows and the number of logs in the 16^{th} row is 5.

We can see that the numbers of logs in rows are in the form of an A.P.20, 19, 18…

For the given A.P.,

*First term, a* = 20 and common difference, _d_ = _a_2−_a_1 = 19−20 = −1

Let a total of 200 logs be placed in _n_ rows.

*Thus, Sn* = 200

By the sum of nth term formula,

\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d}] \\ 200=\frac{\mathrm{n}}{2}(2(20)+(\mathrm{n}-1)(-1)) \\ 400=n(40-n+1) \\ 400=n(41-n) \\ 400=41 n-n 2 \\ n^{2}-41 n+400=0 \\ n^{2}-16 n-25 n+400=0 \\ n(n-16)-25(n-16)=0 \\ (n-16)(n-25)=0 \\ \text { Either }(n-16)=0 \text { or } n-25=0 \\ n=16 \text { or } n=25

By the nth term formula,

*a _{n}* =

*a*_{16} = 20+(16−1)(−1)

*a*_{16} = 20−15

*a*_{16} = 5

Similarly, the 25^{th} term could be written as;

*a*_{25} = 20+(25−1)(−1)

*a*_{25} = 20−24

*a*_{25} = –4

It can be seen, the number of logs in 16^{th} row is 5 as the numbers cannot be negative.

Therefore, 200 logs can be placed in 16 rows and the number of logs in the 16^{th} row is 5.

Lido

Courses

Quick Links

Terms & Policies

Terms & Policies

2021 © Quality Tutorials Pvt Ltd All rights reserved