Question

If the sum of the series 3 + 3x + 3x² + ______ to ∞ is $\frac{45}{8},$ than x = _________.

Answer 1

Sum of series 3 + 3x + 3x² + ______ = $\frac{45}{8}$ (given)
Since a = 3
r = x
and sum of infinite g.p is $\frac{a}{1-r}$
$$\begin{gathered} \therefore \frac{a}{1-r}=\frac{45}{8}\left(\mathrm{given}\right) \\ \Rightarrow \frac{3}{1-x}=\frac{45}{8} \\ 8\times 3=45\left(1-x\right) \\ \mathrm{i}.\mathrm{e}8=15\left(1-x\right) \\ 8=15-15x \\ \mathrm{i}.\mathrm{e}15x=7 \\ \mathrm{i}.\mathrm{e}x=\frac{7}{15} \end{gathered}$$