# Question 11 Exercise 4.2

Solutions of Question 11 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

## Question 11

Ahmad and Akram can climb 1000 feet in the first hour and 100 feet in each succeeding hour. When will they reach the top of a 5400 feet hill?

### Solution

Suppose $a_1$ represent the distance climb by Ahmad and Akram in first hour. Then $$a_1=1000.$$ Distance climb in each succeeding hour $= d=100$.

As the given problem is of A.P with $a_n=5400$, we have to find $n$, which represent the number of hours to reach at top.

We know
\begin{align}
&a_n=a_1+(n-1)d \\
\implies &5400=1000+(n-1)100\\
\implies &5400=900+100n \\
\implies &100n=5400-900\\
\implies &100n=4500\\
\implies &n=45.\end{align}

Hence Ahmad and Akram will take 45 hours to reach at the top of the hill.

### Go To