Answer:
x = -5 * (2)^(n-1)
Step-by-step explanation:
If we look a the supplied n elements of the sequence, and we divide each of them by -5.
1 = -5, -5/-5 = 1
2 = -10, -10/-5 = 2
3 = -20, -20/-5 = 4
4 = -40, -40/-5 = 8
We realize that we have all the powers of 2 there.
So the formula will start with -5 (the first element), then multiplied by a power of 2.
[tex]x = -5 (2)^{n-1}[/tex]
We can verify for the 4th element, where n = 4:
[tex]x = -5 (2)^{n-1} = -5 (2)^{4-1} = -5 (2)^{3} = -5 * 8 = -40[/tex]
