Algebra: Number Series

Question

Explain the pattern

4/3, -2/3, -1/3, 1/6, 1/12, -1/24

The next number is -1/48

6, 3 3/4, 2 1/4, 1 1/4, 3/4, 3/4

The next number is 0

-5/2, -4, -7, -13, -25

Next number is -49

2/5, -3/5, 9/10, -27/20, 81/40, -243/80

Next number is 729/160

Answer 1

I can explain the last pattern. Each number is the previous number multiplied by -3 in the numerator and 2 in the denominator. -3 to the x over 5 * 2^(x-1).

So when x is 2, you'd have -3^(2)/5*2^(1) = 9/10

When x is 3, you'd have -3^(3)/5*2^(2) = -27/20