From the given sequence: 1/4, 2/9, 4,27, 8/81, 16/243 the common ratio is: 2/3 thus the sum of the series will be given by the formula: Sn=[a(1-r^n)]/(1-r) plugging the values we obtain:

Sn=[1/4(1-(2/3)^n)]/(1-2/3) thus the equation that will be used to find the sum is: Sn=3[1/4-1/4(2/3)^n] =3/4[1-(2/3)^n]

## Answers ( 2 )

Answer: Sum of the geometric series will be [tex]frac{763}{972}[/tex]Step-by-step explanation:Since we have given that

[tex]frac{1}{4}+frac{2}{9}+frac{4}{27}+frac{8}{81}+frac{16}{243}[/tex]

Here,

[tex]a=frac{2}{9}r=frac{a_2}{a_1}r=frac{frac{4}{27}}{frac{2}{9}}=frac{4}{27}times frac{9}{2}=frac{2}{3}n=4[/tex]

As we know the formula for

“Sum of n terms in geometric series “:[tex]S_n=frac{a(1-r^n)}{1-r}S_n=frac{frac{2}{9}(1-frac{2}{3}^4)}{1-frac{2}{3}}S_n=frac{130}{243}[/tex]

So, Complete sum will be[tex]frac{130}{243}+frac{1}{4}=frac{520+243}{972}=frac{763}{972}[/tex]

Hence, Sum of the geometric series will be [tex]frac{763}{972}[/tex]From the given sequence:

1/4, 2/9, 4,27, 8/81, 16/243

the common ratio is: 2/3

thus the sum of the series will be given by the formula:

Sn=[a(1-r^n)]/(1-r)

plugging the values we obtain:

Sn=[1/4(1-(2/3)^n)]/(1-2/3)

thus the equation that will be used to find the sum is:

Sn=3[1/4-1/4(2/3)^n]

=3/4[1-(2/3)^n]