Question

The sum of a geometric series is -2044. If the first term is -4 and the common ratio is 2, what is the final term in the sequence?

Answer 1

In a geometric series, the common ratio is the number each term is multiplied by to get the successive term. Hence, this series will be:
-4 + -8 + -16 + ...
You'll notice that the magnitude of the sum of all previous terms is in fact 4 less than the next term in the sequence (so for example, -4 is 4 less than -8, -4 + -8 = -12 is 4 less than -16, -4 + -8 + -16 = -28 is 4 less than - 32, etc)
Thus, if the sum of all terms is -2044, the next term in the sequence would have been -2048. Then the last term in the sequence must have been half that, of -1024.