What are the next 3 terms to this sequence?

2, 6, - 4, 10, - 14, - 24 ...

-38, 62, - 100

Step-by-step explanation:

I think you meant a + 24, not the - 24.

The recursive formula is a_n = a_ (n-2) - a_ (n-1)

so. we try this 3 times after the - 24 term

a_3 = - 4 = 2 - 6 = a_1 - a_2

...

a_6 = a_4 - a_5 = 10 - (-14) = 24

a_7 = a_5 - a_6 = - 14 - (24) = - 38

a_8 = a_6 - a_7 = 24 - (-38) = 62

a_9 = a_7 - a_8 = - 38 - 62 = - 100

a_10 = a_8 - a_9 = 62 - (-100) = 162