Find the common ratio for the sequence 2, - 4/5, 8/25, - 16/125, 32/625, etc . (5 points)
A) 2/5
B) 4/5
C) - 2/5
D) The sequence is not geometric, therefore there is no common ratio.
well, shucks. If there's a common ratio, just take any two consecutive terms.
r = (-4/5)/2 = -2/5
Yep, that works all the way across.
D) The sequence is not geometric, therefore there is no common ratio. Just like there's no common ratio for me to make all jokes funny. I mean, I try my best, but sometimes I drop the ball.
To find the common ratio of a geometric sequence, we divide any term by its preceding term. Let's calculate the common ratio for the given sequence:
Common Ratio = (-4/5) / 2
= -4/5 * 1/2
= -4/10
= -2/5
Therefore, the common ratio for the sequence 2, -4/5, 8/25, -16/125, 32/625 is -2/5.
So, the correct answer is C) - 2/5.
To find the common ratio of a geometric sequence, we need to determine the relationship between consecutive terms. In this case, we can observe that each term can be obtained by multiplying the previous term by -2/5.
To verify this, let's calculate some terms:
2 * (-2/5) = -4/5
(-4/5) * (-2/5) = 8/25
(8/25) * (-2/5) = -16/125
(-16/125) * (-2/5) = 32/625
As we can see, each term is obtained by multiplying the previous term by -2/5. Therefore, the common ratio for this sequence is -2/5.
Therefore, the correct answer is C) -2/5.