Sequences and Series — Maths STD 11 Science — Question
Maharashtra BoardEnglish MediumSTD 11 ScienceMathsSequences and Series1 Mark
Question
For the following G.P.s, find $S_n$ : √5, -5, 5√5, -25, …….
✓
Answer
$a=\sqrt{5}, r=\frac{-5}{\sqrt{5}}=-\sqrt{5}<1$
$S_n=\frac{a\left(1-r^n\right)}{1-r}, \text { for } r<1$
$=\frac{\sqrt{5}\left[1-(-\sqrt{5})^{ n }\right]}{1-(-\sqrt{5})}$
$=\frac{\sqrt{5}}{1+\sqrt{5}}\left[1-(-\sqrt{5})^{ n }\right]$
$=\frac{-\sqrt{5}}{(\sqrt{5}+1)}\left[(-\sqrt{5})^{ n }-1\right]$
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