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Sequences and Series — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsSequences and Series1 Mark
Question
For a G.P.If $S_5=1023, r=4$, find $a$.
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Answer

$ r=4, S_5=1023$
$ S_n=a\left(\frac{r^n-1}{r-1}\right), \text { for } r>1$
$\therefore S_5=a\left(\frac{4^5-1}{4-1}\right)$
$\therefore 1023=a\left(\frac{1024-1}{3}\right)$
$\therefore 1023=\frac{a}{3}(1023)$
$\therefore a=3$

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