Fill in the power-of-two between 64 and 256: 1, 2, 4, 8, 16, 32, 64, ( ? ), 256

Introduction / Context:This is a classic power-of-two sequence. Each term doubles the previous one. Recognizing that exponent pattern lets us insert the missing value instantly.

Given Data / Assumptions:

• Known terms: 1, 2, 4, 8, 16, 32, 64, ( ? ), 256
• Doubling rule holds throughout.

Concept / Approach:Powers of two are 2^0, 2^1, 2^2, … The terms shown run 1, 2, 4, …, 64 (= 2^6), next is 2^7 = 128, then 2^8 = 256.

Step-by-Step Solution:64 * 2 = 128128 * 2 = 256

Verification / Alternative check:Listing exponents: 0,1,2,3,4,5,6,(7),8 confirms the placement.

Why Other Options Are Wrong:148, 154, 164, and 96 are not powers of two and break the doubling pattern.

Common Pitfalls:Mistaking the sequence for an arithmetic progression; here it is geometric (ratio 2).

Final Answer:128