Question

Please please help me

Answer 1

`\large\boxed{\frac{\boxed{8}}{81}}`

Explanation:

`\text{If}\ a_1,\ a_2,\ a_3,\ a_4,\ ...,\ a_n\ \text{is the geometric sequence, then}\\\\(a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)=...=(a_n)/(a_(n-1))=constant=r-\text{common ration}.\\\\\text{We have}\ (1)/(2),\ (1)/(3),\ (2)/(9),\ (4)/(27),\ ...\\\\((1)/(3))/((1)/(2))=(1)/(3)\cdot(2)/(1)=(2)/(3)\\\\((2)/(9))/((1)/(3))=(2)/(9)\cdot(3)/(1)=(2)/(3)\\\\((4)/(27))/((2)/(9))=(4)/(27)\cdot(9)/(2)=(2)/(3)`

`\bold{CORRECT}\\\\(x)/((4)/(27))=(2)/(3)\qquad\text{multiply both sides by}\ (4)/(27)\\\\x=(2)/(3)\cdot(4)/(27)\\\\x=(8)/(81)`