​ What is ∑n=16[4(−5)n−1] equal to?

This  will be the sum of a geometric series where the first term is 4

The common ratio  is -5

And we will have 6 terms.....so....the sum is

first term   [ 1  -  common ratio^number of terms ] / [ 1 - common ratio ]  =

4  [1 - (-5)^6]  /  [ 1  - -5 ]  =

4 [ 1 - 15625 ] / 6  =

(2/3) ( -15624 )  =

-10416