What is the closed form for the sequence (bn) that has the first four terms -16,64,-256,1024

Our author Strogatz shows us something surprising about sums of consecutive counting numbers (integers), starting from 1.What is The sum of the first 6 consecutive integers?     The sum of the first 7 consecutive integers?     The sum of the first 2625 consecutive integers?

Write an expression for the nth term of the sequence 4 8 16 32 22' 32' 42' 52' 6²