SEQUENCES AND SERIES — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSEQUENCES AND SERIES2 Marks
Question
Which term of the sequence 2, 2$\sqrt 2$, 4, .... is 128?
✓
Answer
Here $\mathrm{a}=2, \mathrm{r}=\frac{2 \sqrt{2}}{2}=\sqrt{2}$ and $\mathrm{a}_{\mathrm{n}}=128$
$\therefore a_n=a r^{n-1}$
$\Rightarrow 128=2 \times(\sqrt{2})^{n-1}$
$\Rightarrow 64=(\sqrt{2})^{n-1}$
$\Rightarrow(\sqrt{2})^{12}=(\sqrt{2})^{n-1}$
$\Rightarrow n-1=12$
$\Rightarrow n=13$
Therefore, $13^{\text {th }}$ term of the given G.P. is 128
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