My teacher said I have this backwards,
Here is the question: Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
And here is my answer:
A(n+1) = A(n) * -1/4
An+1 = An * r
is
An+1 = An * (-1/4)
Please correct it
nope. you are quite correct!
Maybe she wants it as
An = An-1 * -1/4
or
An+1 = An/4
For the first?
To formulate the recursive formula for a geometric sequence, you need to identify the common ratio (r) between consecutive terms in the sequence. In this case, the common ratio is -1/4, as each term is multiplied by -1/4 to get the next term.
Now, let's proceed with correcting your answer:
The correct recursive formula for the given geometric sequence is:
A(n+1) = A(n) * (-1/4)
Here's how you can arrive at this formula:
1. Identify the first term: The given sequence starts with -16, so A(1) = -16.
2. Identify the common ratio: By observing the sequence, we can see that each term is multiplied by -1/4 to get the next term. Therefore, the common ratio is -1/4.
3. Write the recursive formula: The recursive formula for a geometric sequence is of the form An+1 = An * r, where An represents the nth term and r represents the common ratio.
Applying this formula to our sequence, we get:
A(n+1) = A(n) * (-1/4)
So, the correct recursive formula for the given geometric sequence {-16, 4, -1, ...} is A(n+1) = A(n) * (-1/4).