Question

G.P 1, 1/a, 1/a2, 1/a3 ___ then nth term is__​

Answer 1

$\textbf{Given:}$

$\textsf{G.P is}$

$\mathsf{1,\dfrac{1}{a},\dfrac{1}{a^2},\dfrac{1}{a^3},\;.\;.\;.\;.}$

$\textbf{To find:}$

$\textsf{n th term of the G.P}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{1,\dfrac{1}{a},\dfrac{1}{a^2},\dfrac{1}{a^3},\;.\;.\;.\;.}$

$\mathsf{Here,}$

$\mathsf{a=1,\;r=\dfrac{1}{a}}$

$\textsf{The n th term of the G.P is}$

$\boxed{\mathsf{t_n=a\,r^{n-1}}}$

$\mathsf{t_n=(1)\left(\dfrac{1}{a}\right)^{n-1}}$

$\implies\boxed{\mathsf{t_n=\dfrac{1}{a^{n-1}}}}$

$\textbf{Find more:}$

Find the four numbers forming a G.P if the second number exceedsthe first by 21 and the fourth number is 336 more than the third.

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