Find the first 4 terms and the 8th term of the recursively-defined sequence.

4. v1 = 0.75 and vn = (-2)vk-1 for n>1

A. 0.75, 1.5, -3, 6; -192

B. -1.5, -3, -6, -12; 192

C. -1.5, -3, -6, -12; -192

D. 0.75, 1.5, 3, 6; -192

E. 1.5, 3, 6, 12; 192

F 0.75, -1.5, 3, -6; 192

Can you also show some of the steps, if possilbe? I'm not sure where to begin.

the terms will be .75 * alternating powers of 2

v_k =
.75 * (-1)^k-1 * 2^(k-1)
.75(1 -2 4 -8 16 -32 64 -128)
so, looks like (F) with a typo.

Thanks Steve!

To find the first 4 terms and the 8th term of the recursively-defined sequence, we need to use the given recursive formula v(n) = (-2) * v(k-1), where v(1) = 0.75 and n > 1.

To start, let's find the second term of the sequence.

v(2) = (-2) * v(1)
v(2) = (-2) * 0.75
v(2) = -1.5

So, the second term of the sequence is -1.5.

Next, let's find the third term of the sequence.

v(3) = (-2) * v(2)
v(3) = (-2) * (-1.5)
v(3) = 3

So, the third term of the sequence is 3.

Continuing, let's find the fourth term of the sequence.

v(4) = (-2) * v(3)
v(4) = (-2) * 3
v(4) = -6

So, the fourth term of the sequence is -6.

Now, we need to find the eighth term of the sequence. Since the recursive formula allows us to find the next term of the sequence by using the previous term, we can use this formula iteratively to find the eighth term.

v(5) = (-2) * v(4)
v(5) = (-2) * (-6)
v(5) = 12

v(6) = (-2) * v(5)
v(6) = (-2) * 12
v(6) = -24

v(7) = (-2) * v(6)
v(7) = (-2) * (-24)
v(7) = 48

v(8) = (-2) * v(7)
v(8) = (-2) * 48
v(8) = -96

So, the eighth term of the sequence is -96.

Now, let us put all the terms together:
First 4 terms: 0.75, -1.5, 3, -6
Eighth term: -96

Looking at the options provided, we can see that the correct answer is option F: 0.75, -1.5, 3, -6; 192.