Question

What is the sum of this geometric series? 16+32+...+256

Answer 1

U1 = a = 16

r = 32/16 = 2

Un = 256

Un = a.r^n-1

256 = 16.2^n-1

2^n-1 = 256/16

2^n-1 = 16

2^n-1 = 2^4

n-1 = 4

n = 5

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

S5 = 16(2^5 - 1) / 2-1

S5 = 16(31)

S5 = 496