# Question 28 and 29, Exercise 4.4

Solutions of Question 28 and 29 of Exercise 4.4 of Unit 04: Sequence and Series. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

## Question 28

A super ball dropped from the top of the tower (556 ft high) always rebounds three-fourths of the distance fallen. How far (up and down) will the ball have travelled when it hits the ground for the 6th time?

** Solution. **

## Question 29

The teaching staff of high school informs its members of school cancellation by telephone. The principal calls 2 teachers, each of whom in turn calls 2 other teachers, and so on. In order to inform the entire staff, 6 rounds of calls are made. Counting the principal, find how many people are in staff at high school?

** Solution. **
We have given

first person $=a_1= 1$ principal

People in first round $= a_2 = 2$

People in 2nd round $= a_3 = 2(2)=4$

…

People in 6ht round $= a_7$.

Thus we have the series
$$
1+2+4+...+a_7
$$
We have to find sum of geometric series with $a_1=1$, $r=2$, $n=7$.

As we have $$ S_n=\frac{a_1\left(1-r^n \right)}{1-r}, \quad r\neq 1. $$ Thus \begin{align*} S_6&=\frac{(1)\left(1-2^7 \right)}{1-2} \\ &=\frac{1-128}{-2}\\ &=127 \end{align*} Hence 127 people are in staff at high school.

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