Sequences and Series (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question
Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Sequences and Series (p-1)1 Mark
Question
Verify whether the following sequences are G.P. If so, write tn. : $1,-5,25,-125$,
✓
Answer
$1,-5,25,-125, \ldots \ldots$ $t_1=1, t_2=-5, t_3=25, t_4=-125, \ldots$. Here, $\frac{t_2}{t_1}=\frac{t_3}{t_2}=\frac{t_4}{t_3}=-5$ Since, the ratio of any two consecutive terms is a constant, the given sequence is a geometric progression. Here, $a=1, r=-5$ $ \begin{aligned} & t_n=a r^{n-1} \\ & \therefore t_n=(-5)^{n-1} \end{aligned} $
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