====== Question 16 and 17, Exercise 4.4 ======
Solutions of Question 16 and 17 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 16=====
Find the nth term of the geometric sequence if $a_{1}=7, n=4, r=2$

** Solution. **

Given $a_{1}=7$, $n=4$, $r=2$.\\
General term of the geometric series is given by
$a_{n}=a_{1} r^{n-1}.$
Thus
\begin{align*}
a_4 &= 7 \times 2^{4-1} \\ 
&= 7 \times 2^3 \\ 
&= 7 \times 8 = 56.
\end{align*}
Hence $a_4=56$.

=====Question 17=====
Find the nth term of the geometric sequence if $a_{1}=243, n=5, r=-\frac{1}{3}$

** Solution. **

Given $a_{1}=243$, $n=5$, $r=-\frac{1}{3}$.\\
General term of the geometric series is given by
$a_{n}=a_{1} r^{n-1}.$
Thus
\begin{align*}
a_5 &= 243 \times \left(-\frac{1}{3}\right)^{5-1} \\ 
&= 243 \times \left(-\frac{1}{3}\right)^{4} \\ 
&= 243 \times \frac{1}{81} \\ 
&= 3.
\end{align*}
Hence $a_5=3$.






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