How to use algebra to find sum of geometric series 1+(-2)+4+(-8)+...256

Find the sum of the finite geometric series 1+(-2)+4+(-8)+...256 by using algebra or formula

Please help out with the solution or formula, I wasn't able to find one in textbook, thanks

first term, a = 1

common ratio, r = -2

a_n = 256

=> ar^(n-1) = 256

=> 1(-2)^(n-1) = 256

=> (-2)^(n-1) = 2^8

=> 2^(n-1) = 2^8 (since 256 is positive, n - 1 is even )

=> n - 1 = 8

n = 9

Sn = a(r^n - 1) /(r - 1)

= 1((-2^9) - 1)/(-3) = -513/-3 = 171