Question 14 and 15, Exercise 4.2
Solutions of Question 14 and 15 of Exercise 4.2 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 14
Find '$b$' if $10$ is A.M between $b$ and $20$.
Solution.
Let $a= b$ and $b=20$. Then
\begin{align*}
&\text{A.M.} = \frac{a + b}{2} \\
\implies & 10 = \frac{b + 20}{2} \\
\implies & 20 = b + 20 \\
\implies & b = 20 - 20 \\
\implies & b = 0
\end{align*}
Hence $b = 0$.
- Find '$b$' if $25$ is A.M between $b$ and $20$.
- Find '$b$' if $10$ is A.M between $b$ and $-10$.
Question 15
Find $x$ and $y$ if $2$ and $13$ are two arithmetic means between $x$ and $y$.
Solution.
Given: $2$ and $13$ are two arithmetic means between $x$ and $y$.
This gives $x$, $2$, $13$, $y$ are in A.P.
Here $a_1 = x$ and $d=13-2=11$.
Now
\begin{align*}
& a_2= a_1+d\\
\implies &2 = x + 11 \\
\implies & \boxed{x=-9}
\end{align*}
Also
\begin{align*}
&a_4=a_1+3d\\
\implies &y=x+3(11)\\
\implies &y=-9 + 33 \\
\implies &\boxed{y=24}\end{align*}
Hence $x=-9$ and $y=24$.
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