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What is the sum of the geometric sequence 2, 8, 32, … if there are 8 terms? 21,845
43,690
65,535
87,380

Respuesta :

Answer:

The answer is B. 43,690

Step-by-step explanation:

S = 2 * 4^0 + 2 * 4^1 + 2 * 4^2 + ... + 2 * 4^7

S * 4 = 2 * 4^1 + 2 * 4^2 + ... + 2 * 4^7 + 2 * 4^8


4S - S = 2 * 4^8 - 2 * 4^0

3S = 2 * (4^8 - 1)

S = (2/3) * (4^8 - 1)

S = (2/3) * (2^16 - 1)

S = (2/3) * (65535)

S = 43690

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