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.

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: $$\begin{align*} &16+16+16+\ldots \text{ to 11 terms}\\ =&11(16) \\ =& 176 \end{align*}$$

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 $93.75$.

Question 3 and 4 >