Write the first three terms of the G.P. whose first term and the … - Vidyadip

Question

Write the first three terms of the G.P. whose first term and the common ratio are given below
$a=\sqrt{2}, r=\sqrt{2}$

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Answer

$a=\sqrt{2}, r=\sqrt{2} $
$t_n=a^{n-1} $
$t_1=\operatorname{ar}^{1-1}=a^0=\sqrt{2} \times 1=\sqrt{2} $
$t_2=\operatorname{ar}^{2-1}=\operatorname{ar}^1=\sqrt{2} \times \sqrt{2}=2 $
$t_3=\operatorname{ar}^{3-1}=\operatorname{ar}^2=\sqrt{2} \times(\sqrt{2})^2 $
$=\sqrt{2} \times 2=2 \sqrt{2}$
$\therefore$ The 3 terms are $\sqrt{2}, 2,2 \sqrt{2}, \ldots$

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