Question

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

Answer 1

the actual answer is
`a_(n)`
`=((2)/(9) )3^(n-1)`

test taken, I know the real numbers for the question, and the real answer, and this is it

Answer 2

Tn = 2/3^(n-1)

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)