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Sequences and Series (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Sequences and Series (p-1)2 Marks
Question
In a G.P., if $t_2=7, t_4=1575$, find $r$.
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Answer

$\begin{array}{ll} & \text { Given } \mathrm{t}_2=7, \mathrm{t}_4=1575 \\ & \mathrm{t}_{\mathrm{n}}=a \mathrm{ar}^{\mathrm{n}-1} \\ \therefore & \mathrm{t}_2=\mathrm{ar} \\ \therefore & 7=\mathrm{ar} \\ \therefore & \mathrm{a}=\frac{7}{\mathrm{r}} \\ \therefore & \mathrm{t}_4=\mathrm{ar}^3 \\ \therefore \quad & \mathrm{ar}^3=1575 \\ \therefore & \mathrm{r}^3 \times\left(\frac{7}{\mathrm{r}}\right)=1575 \\ \therefore & \mathrm{r}^2 \times 7=1575 \\ \therefore & \mathrm{r}^2=\frac{1575}{7} \\ \therefore & \mathrm{r}^2=225 \\ \therefore & \mathrm{r}= \pm 15\end{array}$

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