nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... me.
=====Question 27=====
A city has a current population of 100,000 and the population is increasing by $3 \%$ each year. What will the population be in $15^{\text {th }}$ years?
** Solutio
nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... n*}
1 = (3k+1)A+(3k-2)B \ldots (2)
\end{align*}
Put $3k-2=0$ $\implies k=\dfrac{2}{3}$ in (2), we ha... 0 \\
\implies &A = \frac{1}{3}.
\end{align*}
Now put $3k+1=0$ $\implies k=-\dfrac{1}{3}$ in (2), we h... n*}
1 = (5k+1)A+(5k-4)B \ldots (2)
\end{align*}
Put $5k-4=0$ $\implies k=\dfrac{4}{5}$ in (2), we ha
nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... {align*}
1 = A(k+2) + Bk \ldots (2)
\end{align*}
Put $k=0$ in (2), we have
\begin{align*}
&1=2A + 0 \\
\implies & A = \frac{1}{2}.
\end{align*}
Put $k+2=0 \implies k=-2$ in (2), we have
\begin{ali... n*}
1 = (3k+1)A+(3k-2)B \ldots (2)
\end{align*}
Put $3k-2=0$ $\implies k=\dfrac{2}{3}$ in (2), we ha
nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... &\\
\implies \boxed{d = -3} \quad \\
\end{align*}
Putting the value $d$ in (1)
\begin{align*}
& a_1 +1... &\\
\implies \boxed{d = 4} \quad \\
\end{align*}
Putting the value $d$ in (1)
\begin{align*}
& a_1 +
nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder...
1 = (k+2)A + (k+1)B \ldots (2)
\end{align*}
Now, put $k+1=0 \implies k=-1$ in equation (2):
\begin{al... -1+2)A + 0 \\
\implies A &= 1.
\end{align*}
Next, put $k+2=0 \implies k=-2$ in equation (2):
\begin{al
nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... = (2k+9)A + (2k+3)B \ldots (2)
\end{align*}
Now, put $2k+3 = 0 \implies k = -\frac{3}{2}$ in equation... \\
\implies A &= \frac{1}{6}.
\end{align*}
Next, put $2k+9 = 0 \implies k = -\frac{9}{2}$ in equation
nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... **
Given:
$$a_n = (-1)^{n+1}(3n - 5).$$
we can compute the following terms:
\begin{align*}
a_1 &= (-1)
nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... s \boxed{d = -\frac{5}{2}} \quad \\
\end{align*}
Putting the value $d$ in (1)
\begin{align*}
& a_1 +
nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... \frac{a+c}{ac}\\
b&= \frac{a+c}{2ac}
\end{align*}
Putting the value of $b$ in (i), we have\\
\begin{al