Question

The explicit formula for the geometric sequence -1/9,1/3,-1,3,-9

Answer 1

ANSWER



`\boxed {a_n= - (1)/(9) {( - 3)}^(n - 1) }`


Step-by-step explanation

The given geometric sequence is



`- (1)/(9) , (1)/(3) , - 1,3, - 9,...`


The first term of the geometric sequence is,


`a_1= - (1)/(9)`

and there is a common ratio of


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


The explicit formula, for the geometric sequence is given by,



`a_n=a_1 {r}^(n - 1)`



We substitute the values into the formula to get the explicit formula as,



`a_n= - (1)/(9) {( - 3)}^(n - 1)`