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

Answer:

$c(n)=4\cdot(-\frac{1}{3})^{n-1}$

Explanation:

In the given geometric sequence:

$4,-\frac{4}{3},\frac{4}{9},-\frac{4}{27},\frac{4}{81},\ldots$

We see that:

• The first term, c1 = 4

Also:

$-\frac{4}{3}\div4=-\frac{4}{3}\times\frac{1}{4}=-\frac{1}{3}$

• 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:

$c(n)=4\cdot(-\frac{1}{3})^{n-1}$