Find the sum of the first 6 terms in the sequence -5 -25 -125 -625

This is a geometric sequence, so use the formula for the sum of a geometric sequence:
Sum = (a(r^n - 1))/(r - 1)
where a is the first term, -5
r is the common ratio, 5
and n is the number of terms

Thus,
Sum = ((-5)(5^6 - 1))/(5-1) = -19530