Question

Find the 20th and n th terms of the G.P. $\frac{5 }{ 2} ,\frac{ 5}{ 4} ,\frac{ 5 }{ 8}$,......

Answer 1

The given G.P. is $\frac{5 }{ 2} ,\frac{ 5}{ 4} ,\frac{ 5 }{ 8}$,......
Here, a = First term =$\frac{ 5 }{ 2}$ $=\frac{\frac{5}{4} }{5} = \frac{1 }{ 2}$
r = Common ratio = 2
a20 = ar 20-1 = $\frac{5 }{ 2} (\frac{1 }{ 2})^{19} = \frac{5 }{(2)(2)^{19}} =\frac{ 5 }{ (2)^{20}}$
an = arn - 1 = $\frac{5 }{ 2} (\frac{1 }{ 2})^{n-1} = \frac{5 }{(2)(2)^{n-1}} =\frac{ 5 }{ (2)^{n}}$