write the next term in the sepuence. then write a rule for the nth term.?

Question

7,-8,9,-10,.....

1/2, -1/4, 1/8, -1/16,......

Answer 1

11+....((-1)^n)(n+7)

1/32...((-1)^n)(1/(2^(n+1)))

Answer 2

7,-8,9,-10,.....
Add 1 then change sign of the previous

nth term = (6 + n)x(-1)^(n+1)
(-1)^(n+1) = 1 for odd, and -1 fo even

1/2, -1/4, 1/8, -1/16,......
just changing sign and multiplying each with 1/2

nth term is
[(1/2)^(n)] x [(-1)^(n+1)]

Answer 3

The trick for alternating + - sequences is to use (-1)^n or (-1)^(n+1) depending if even or odd terms are to be positive.

[(-1)^(n)]*(6+n)
next 11

[(-1)^(n)]*[1/(2^n)]
next 1/32

Answer 4

11, a(n) = (6 + n) * (-1)^(n+1)

1/32, a(n) = [1/(2^n)] * (-1)^(n+1)