====== Question 15 and 16, Exercise 4.1 ======
Solutions of Question 15 and 16 of Exercise 4.1 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 15=====
Find the indicated term of the sequence. $a_{n}=4 n^{2}(11 n+31) ; a_{22}$

** Solution. **
Given: $$a_n = 4n^2(11n + 31).$$ Then
\begin{align*}
a_{22} &= 4 \cdot 22^2 \cdot (11 \cdot 22 + 31) \\
&= 4 \cdot 484 \cdot (242 + 31) \\
&= 4 \cdot 484 \cdot 273 \\
&= 4 \cdot 132132 \\
&= 528528
\end{align*}
Hence $a_{22} = 528528$. GOOD

=====Question 16=====
Find the indicated term of the sequence. $a_{n}=\left(1+\frac{1}{n}\right)^{2} ; a_{20}$

** Solution. **
Given: $$a_n = \left(1 + \frac{1}{n}\right)^2.$$ Then
\begin{align*}
a_{20} &= \left(1 + \frac{1}{20}\right)^2 \\
&= \left(\frac{20 + 1}{20}\right)^2 \\
&= \left(\frac{21}{20}\right)^2 \\
&= \frac{441}{400}
\end{align*}
Hence $a_{20}=\frac{441}{400}$. GOOD



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