If 2nd term of a G.P. is 24 and 5th term is 81, then the first term is

16

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18

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21

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12

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Solution

The correct option is A $16$
2nd term in GP is $a r = 24$
5th term in GP is $a r^{4} = 81$
Dividing both the equations, we get,
$r^{3} = \frac{81}{24}$

Also, $a^{3} r^{3} = (24)^{3}$ $[a r = 24]$
$\Rightarrow a^{3} r^{3} = 2^{9} \times 3^{3}$
$∴ a^{3} = \frac{24}{81} \times 2^{9} \times 3^{3}$

$\Rightarrow a^{3} = \frac{2^{12} \times 3^{3}}{3^{4}}$

$\Rightarrow a^{3} = (2^{4})^{3}$
Hence, $a = 2^{4} = 16$

Hence, the first term is, $a = 16$

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