Question

Complete the explicit and recursive formula of the geometric sequence

56, -28, 14, -7
put your explicit function in it simplest form.
Explicit: a(n)= __*(__)^n
Recursive: a1=__; a(n)=a(n-1)*__

Answer 1

To find the explicit and recursive formulas for the geometric sequence 56, -28, 14, -7, the common ratio should be determined. The common ratio can be obtained by dividing any term by its previous term. The explicit formula is a(n) = 56 * (1/2)^(n-1) and the recursive formula is a(1) = 56, a(n) = a(n-1) * (1/2).

Step-by-step explanation:

To find the explicit formula of the given geometric sequence, we need to determine the common ratio (r). The common ratio can be found by dividing any term in the sequence by its previous term. In this case, -28/-56 = 1/2. Therefore, the common ratio is 1/2.

Now we can use the formula for a geometric sequence to find the explicit formula:

Explicit formula: a(n) = 56 * (1/2)^(n-1)

The recursive formula can be obtained by expressing each term in the sequence in terms of the previous term:

Recursive formula: a(1) = 56, a(n) = a(n-1) * (1/2)