Question

Khaled and Wilma were asked to find an explicit formula for the sequence 1, 3, 9, 27. Khaled said the formula is f(n)=1*3^n-1 and Wilma said the formula is f(n)=1*3^n. Which one of them is right?

Answer 1

khaled is correct. f(n)=1x3^n-1

Explanation:

Answer 2

`f(n) = 1 * ( {3}^(n - 1) )`

EXPLANATION

The given sequence is 1, 3, 9, 27...

The first term of this sequence is

`a = 1`

The common ratio is

`r = (3)/(1) = (9)/(3) = (27)/(9) = 3`

The explicit formula for this geometric sequence is

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

We substitute the first term and the common ratio to obtain,

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