Question

Find the formula for the nth term for the following sequence.

3, 9, 27, 81..

1. A(n) =3(3^n-1)
2. A(n) =3^n-1
3. A(n) =3(3^n)

Answer 1

It is 1. A(n) =3(3^n-1)

Explanation:

It is a geometric progression

General recursive formular:

`a_(n) = a( {r}^(n-1) )`

a » first term, a = 3

r » common difference, r = 9 ÷ 3 = 3

n » number of terms

`A(n) = 3( {3}^(n-1) )`

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further more:

`A(n) = {3}^((n))`

Answer 2

Explanation:

everything can be found in the picture