====== Question 30, Exercise 4.4 ======
Solutions of Question 30 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 30=====
A 5-day rain caused the river to rise. After the first day, the river rose one inch. Each day the rise in the river tripled. How much had the river risen after 5 days?

** Solution. **

Suppose rise in river: 

after 1st day $=a_1= 1$ inch\\
after 2nd day $=a_2= 3$ inch \\
after 3rd day $=a_3=3\times 3 = 9$ inch\\
after 4th day $=a_4=3\times 9 = 27$ inch\\
after 5th day $=a_5=3\times 27 = 81$ inch.

Hence the river will rise $81$ inch after five days. GOOD

**Alternative Method:**

Take $a_1=1$ and $r=3$. 

Then rise in river after five day $a_5=?$

From the given data, we have geometric sequence with
$$a_n=a_1 r^{n-1}.$$
implies
\begin{align*}
a_5&=a_1 r^4 \\
&=(1)(3)^4 = 81
\end{align*}
Hence river will rise 81 inch after five days. GOOD

<callout type="warning" icon="true">
If one conclude that the rise in river is with respect to the previous day. Then the total rise in river after five days will be
$$S_n=a_1+a_2+a_3+a_4+a_5.$$
</callout>

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