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.

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?

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.

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