Question

find th 20th and nth terms of the gp 5/2,5/4,5/8,......

Answer 1

it is your answer thanks for your

Answer 2

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Given ,

$\star$First term (a) = 5/2

$\star$Common difference (r) = 1/2

We know that , nth term of GP is

$\large \sf \fbox{ \fbox{ a_{n} = a {(r)}^{n - 1}} }$

So , 20th term of the given GP :

$\sf \implies a_{20} = \frac{5}{2} \times {( \frac{1}{2} )}^{20 - 1} \\ \\ \sf \implies a_{20} = \frac{5}{2} \times { (\frac{1}{2}) }^{19} \\ \\ \sf \implies \fbox{ a_{20} = \frac{5}{ {(2)}^{20} } }$

n term of the given GP :

$\sf \implies \fbox{a_{n} = \frac{5}{2} \times {( \frac{1}{2} )}^{n - 1} }$