# Question 1 and 2, Exercise 4.5

Solutions of Question 1 and 2 of Exercise 4.5 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 1

Find the sum of the geometric series. $16+16+16+\ldots$ to 11 terms.

** Solution. **

In this geometric series $a_1=16$ and $r=\dfrac{16}{16}=1$. Formula of geometric series is applicable if $r\neq 1$. Thus we do directly as follows: \begin{align*} &16+16+16+\ldots \text{ to 11 terms}\\ =&11(16) \\ =& 176 \end{align*}

## Question 2

Find the sum of the geometric series. $75+15+3+...$ to 10 terms.

** Solution. **

Given: $75+15+3+...$ to 10 terms.

Here $a_1= 75$, $r = \frac{15}{75} = \frac{1}{5}$, $n = 10$.

The formula to find the sume of $n$ terms of geometric series $$ S_n = \frac{a_1 \left(1 - r^n\right)}{1 - r}, \quad r\neq 1.$$ Thus \begin{align*} S_{10} &= \frac{75\left(1 - (\frac{1}{5})^{10}\right)}{1 - \frac{1}{5}} \\ &= \frac{75\left(1\right)}{0.8} \\ &=93.75 \end{align*} Hence the required sum is $93.75$.

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