Sequences and series

Question

What's the nth term of the sequence 9/1, -12/2, 15/6, -18/24....?

Answer 1

denominator goes 1,2,6,24, ...

numerator goes 9,12,15,18,21, ... with alternating sign, odd terms positive, evens negative, an AP with d=3

nth term = nu/d where nu =9+3(n-1) = 3n+6

and d may be exponential with a=1/12, b=4, c=8/12

d =ab^(n) +c

1 =4/12+8/12 = 1

2 =16/12+8/12 =2

6 = 64/12+8/12 =6

nth term =nu/d

= (3n+6)/(1/12)(4^n)+8/12)(-1)^(n-1))

=36(n+2)/((4^n+8)(-1)^(n-1))