For a geometric progression, T_1 ^2=T_2 and T_3=64. Write the seq… - Vidyadip

Question

For a geometric progression, $T_1{ }^2=T_2$ and $T_3=64$. Write the sequence.

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Answer

Here, $T_1^2=T_2 ; T_3=64$
$T_n=a \cdot r^{n-1}$
$T_1=a$
$T_2=a r$
$T_3=a r^2$
$\left(T_1\right)^2=T_2$
$(a)^2=a r$
$a=r$
$T_3=a r^2$
$64=r \cdot r^2$
$64=r^3$
$(4)^3=r^3$
$r=4$
$a=r: a=4$
First term $=4$ and common ratio $r=4$
Hence, the sequence obtained is $4,16,64, \ldots$

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