Question

Find the explicit formula for the geometric sequence given below. c1= 4. The sequence is: 4, - 4/3, 4/9, - 4/27, 4/81.

Answer 1

`c(n)=4\cdot(-(1)/(3))^(n-1)`

Step-by-step explanation:

In the given geometric sequence:

`4,-(4)/(3),(4)/(9),-(4)/(27),(4)/(81),\ldots`

We see that:

• The first term, c1 = 4

Also:

`-(4)/(3)/4=-(4)/(3)*(1)/(4)=-(1)/(3)`

• The common ratio, r= -1/3

The explicit formula for a geometric function is obtained using the formula:

`f(n)=a\cdot r^(n-1)`

Substituting a (the first term, c(1)) and r, we have the explicit formula below:

`c(n)=4\cdot(-(1)/(3))^(n-1)`