Question

What is the 7th term of the geometric sequence where a1 = 1,024 and a4 = -16?

Answer 1

a) 1
b) -0.25
c) -1
d) 0.25

Answer 2

d.

Answer 3

So we just need to somehow recognize the pattern going on here. If the first term is positve and the 4th term is negative, then you can see that the signs of each term alternate. So that being said, if the 4th term is negative, the 5th is positive, 6th is negative, and 7th is positive. Meaning you are only left with either A or D. So, now we need to see how do we get from 1024 to -16 in 3 operations. The way we got there is by dividing by -4 every time. So if we divide -16 by -4 3 additional times, we go from -16 to 4 to -1 to .025.