Write the terms of the $G P$ when the first term $a$ and the common ratio $r$ are given?
(i) $a = 4; r = 3$
(ii) $a \sqrt{5}, r = \frac{1}{5}$

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Solution

As we know that, in a G.P.-
$a_{n} = a r^{n - 1}$
Therefore,
(i) $a = 4; r = 3$
First term $= 4$
$a_{2} = a r = 4 \times 3 = 12$
$a_{3} = a r^{2} = 4 \times 3^{2} = 36$
(ii) $a = \sqrt{5}; r = \frac{1}{5}$
First term $= \sqrt{5}$
$a_{2} = a r = \sqrt{5} \times \frac{1}{5} = \frac{\sqrt{5}}{5} = \frac{1}{\sqrt{5}}$
$a_{3} = a r^{2} = \sqrt{5} \times {(\frac{1}{5})}^{2} = \frac{\sqrt{5}}{25} = \frac{1}{5 \sqrt{5}}$

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Write the terms of the GP when the first term a and the common ratio r are given?(i) a=4;r=3(ii) a√5,r=15

As we know that, in a G.P.-an=arn−1Therefore,(i) a=4;r=3First term =4a2=ar=4×3=12a3=ar2=4×32=36(ii) a=√5;r=15First term =√5a2=ar=√5×15=√55=1√5a3=ar2=√5×(15)2=√525=15√5

Write the terms of the $G P$ when the first term $a$ and the common ratio $r$ are given?
(i) $a = 4; r = 3$
(ii) $a \sqrt{5}, r = \frac{1}{5}$