Find the sum of the first five terms of the geometric series in which a2 is -12 and a5 is 768.

  615

Step-by-step explanation:

The ratio of the given terms can be used to find the common ratio between terms:

  a5/a2 = (a1·r^(5-1))/(a1·r^(2-1)) = r^3 = 768/-12 = -64

  r = ∛-64 = -4

So the first term is ...

  a1 = a2/r = -12/-4 = 3

And the first 5 terms of the series are ...

  3 + (-12) + (48) + (-192) + 768 + ...

The sum of the first 5 terms is 615.

40 is the final : )

i think the answer is seven, for if i'm being useless °ω°

step-by-step explanation: