Verify whether the following sequences are G.P. If so, write tn. … - Vidyadip

Question

Verify whether the following sequences are G.P. If so, write tn. : $3,4,5,6, \ldots \ldots$

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Answer

$3,4,5,6, \ldots \ldots$
$t_1=3, t_2=4, t_3=5, t_4=6, \ldots$.
Here, $\frac{\mathrm{t}_2}{\mathrm{t}_1}=\frac{4}{3}, \frac{\mathrm{t}_3}{\mathrm{t}_2}=\frac{5}{4}, \frac{\mathrm{t}_4}{\mathrm{t}_3}=\frac{6}{5}$
Since, $\frac{t_2}{t_1} \neq \frac{t_3}{t_2} \neq \frac{t_4}{t_3}$
$\therefore$ the given sequence is not a geometric progression.

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