Question
Mathematics Question on Sequence and series
An infinite GP has first term x and sum 5, then x belongs to
A
x < - 10
B
-10 < x < 0
C
0 < x < 10
D
x > 10
Answer
0 < x < 10
Explanation
Solution
We know that, the sum of infinite terms of GP is
\hspace20mm S_\infty =\Bigg\\{ \begin{array}
\\\ \frac{a}{1-r} ,\\\
\ \infty \ \, \\\
\end{array}
\begin{array}
\\\ |\ r \ | < 1 \\\
|\ r \ | \ge 1 \\\
\end{array}
\therefore \hspace10mm S_\infty = \frac{x}{1-r} = 5 \hspace35mm [| r | <1]
or \hspace10mm 1-r =\frac{x}{5}
\Rightarrow \hspace15mm r= \frac{5-x}{5} exists only when | r | < 1.
i.e. $\hspace15mm -1