Finding sum of geometric series

Question

24 + (−12) + 6 + ⋯

S=????

Answer 1

-12/24 = -1/2, 6/(-12) = -1/2, ...

The series 24 + (-12) + 6 + ... is geometric with a₁ = 24 and r = -1/2.

Since r is in the interval (-1,1), The series has a finite sum, S given by:

S = a₁ / (1-r) = 24 / (3/2) = 16