Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
A(n+1) = A(n) * -1/4
An+1 = An * r
is
An+1 = An * (-4)
I mean (-1/4)
To find the recursive formula for a geometric sequence, we need two pieces of information: the first term of the sequence (denoted as "a"), and the common ratio between consecutive terms (denoted as "r").
In this case, the first term, a, is -16, and the common ratio, r, can be calculated by dividing any term by its preceding term. Let's choose the second term, 4, and divide it by the first term, -16:
r = 4 / (-16) = -1/4.
Now that we have both a and r, we can write the recursive formula:
a(n) = a(n-1) * r
Where a(n) represents the nth term of the sequence, a(n-1) represents the preceding term, and r is the common ratio.
Thus, for the given geometric sequence {-16, 4, -1, ...}, the recursive formula is:
a(n) = a(n-1) * (-1/4)