====== Question 12 & 13 Exercise 4.2 ======
Solutions of Question 12 & 13 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

=====Question 12=====
A man earned dollars 3500 the first year he worked. If he received a raise
of dollars 750 at the end of each year for 20 years, what was his salary during his twenty first year of work? GOOD
====Solution====
Suppose $a_1$ represents salary of worker at first year. Then
$$a_1=3500.$$
Increase in salary in each year $=d=750$.
The given problem is of A.P and we have to find $a_{21}$.

As, we have
\begin{align}
a_{21}&=a_1+20d\\
&=3500+20(750) \\
&=18500. \end{align}
Hence, the salary of the man during his 21st year of work is dollars 18,500. GOOD

=====Question 13(i)=====
Find the arithmetic mean between $12$ and $18$. GOOD
====Solution====
Here $a=12, b=18$.\\
Let say $A$ be arithmetic means. Then \\
\begin{align}A&=\dfrac{a+b}{2}\\&=\dfrac{12+18}{2}\\&=\dfrac{30}{2}=15.\end{align}
Hence 15 is A.M between 12 and 18. GOOD

=====Question 13(ii)=====
Find the arithmetic mean between $\dfrac{1}{3}$ and $\dfrac{1}{4}$.
====Solution====
Here $a=\dfrac{1}{3}, b=\dfrac{1}{4}$,\\
Let $A$ be arithmetic mean. Then\\
\begin{align}A&=\dfrac{a+b}{2}\\&=\dfrac{\dfrac{1}{3}+\dfrac{1}{4}}{2}\\&=\dfrac{\dfrac{4+3}{12}}{2}\\&=\dfrac{7}{24}\end{align}
GOOD

=====Question 13(iii)=====
Find the arithmetic mean between $-6,-216$. GOOD
====Solution====
Here $a=-6, b=-216$.\\ 
Let $A$ be arithmetic mean. Then\\
$$A=\dfrac{a+b}{2}=\dfrac{-6-216}{2}=-111$$
GOOD

=====Question 13(iv)=====
Find the arithmetic mean between $(a+b)^2,(a-b)^2$. GOOD
====Solution====
 Here $a^{\prime}=(a+b)^2$, $b^{\prime}=(a-b)^2$.\\
Let $A$ be arithmetic mean. Then\\
\begin{align}
A&=\dfrac{a^{\prime}+b^{\prime}}{2}\\
&=\dfrac{(a+b)^2+(a-b)^2}{2} \\
\Rightarrow A&=\dfrac{a^2+b^2+2 a b+a^2+b^2-2 a b}{2} \\
& =\dfrac{2a^2+2b^2}{2}\\
&=a^2+b^2.\end{align}
GOOD

====Go To====
<text align="left"><btn type="primary">[[math-11-kpk:sol:unit04:ex4-2-p8 |< Question 11 ]]</btn></text>
<text align="right"><btn type="success">[[math-11-kpk:sol:unit04:ex4-2-p10|Question 14 >]]</btn></text>