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
$a=1000, r=\frac{2}{5}$

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Answer

$a=1000, r=\frac{2}{5} $
$t_n=a r^{n-1} $
$t_1=a r^{1-1}=a r^0=1000 \times 1=1000 $
$t_2=\operatorname{ar}^{2-1}=a r=1000 \times \frac{2}{5}=400 $
$t_3=a^{3-1}=\operatorname{ar}^2=1000\left(\frac{2}{5}\right)^2 $
$=1000 \times \frac{4}{25} $
$=160$
$\therefore$ The $3$ terms are $1000,400,160, \ldots \overline{ A }$

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