Choose the correct recursive formula for the Geometric Sequence.
2, -8, 32, -128, 512,
32 = -4 * 8
-128 = -4 * 32 etc
so I claim
an = 2 * (-4)^(n-1)
To find the recursive formula for a geometric sequence, we need to find the common ratio between consecutive terms. The common ratio is found by dividing any term in the sequence by its previous term.
Let's take the second and first terms of the sequence:
-8 / 2 = -4
Now, let's take the third and second terms of the sequence:
32 / (-8) = -4
Similarly, for the fourth and third terms of the sequence:
-128 / 32 = -4
And for the fifth and fourth terms of the sequence:
512 / (-128) = -4
From these calculations, we can see that the common ratio between consecutive terms in this sequence is -4.
The recursive formula for a geometric sequence is written in the form:
a(n) = r * a(n-1)
where:
- a(n) represents the nth term in the sequence,
- r represents the common ratio,
- a(n-1) represents the previous term in the sequence.
Applying this to our sequence, where a(1) = 2 (first term) and r = -4 (common ratio), we can write the recursive formula as:
a(n) = -4 * a(n-1)
Therefore, the correct recursive formula for the given geometric sequence is:
a(n) = -4 * a(n-1)