What is the explicit rule for this geometric sequence? 2/9,2/3,2,6,...

an=3(29)n−1

an=3(29)n

an=29⋅3n−1

an=29⋅3n

Tn = 2/3^(n-1)

Step-by-step explanation:

The nth term of a geometric progression is expressed as

Tn = ar^{n-1}

a is the first term

n is the number of terms

r is t common ratio

From the sequence

a = 2/9

r = (2/3)/(2/9) = 2/(2/3) =3

Substitute

Tn = 2/9(3)^(n-1)

Tn = 2/3^(n-1)

Hence the required equation is Tn = 2/3^(n-1)

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

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