1,-2,3,-4,5 ...

what's the next two numbers in the pattern?

The two numbers following 1,-2,3,-4,5 ... are - 6 and 7.

Step-by-step explanation:

index: 1 2 3 4 5 ...

value: 1 - 2 3 - 4 5

Let the index be n. Then the first term is a (1), the secon is a (2), and so on.

a (2) = 2 * (-1) ^ (2-1) = 2 * (-1) = - 2 (correct)

a (3) = 3 * (-1) ^ (3-1) = 3 * (-1) ^2 = 3 (correct)

a (4) = 4 * (-1) ^ (4-1) = 4 * (-1) ^3 = - 4 (correct)

So the general formula for a (n) is: a (n) = n (-1) ^ (n-1)

Thus,

a (5) = 5 (-1) ^4 = 5

a (6) = 6 (-1) ^5 = - 6

a (7) = 7 (-1) ^6 = 7

The "next two numbers in the pattern" are - 6 and 7. The first 7 numbers are

1,-2,3,-4,5, - 6, 7