Number series — determine the next term. Sequence: 2, 8, 16, 128, ?

Introduction / Context:
This item examines recognition of multiplicative jumps driven by powers of 2. Many exam series interleave different multipliers; spotting the power pattern quickly leads to the correct continuation.

Given Data / Assumptions:

• Terms: 2, 8, 16, 128, ?
• All given terms are powers of 2 or products that can be expressed with powers of 2.
• We look for a multiplier pattern consistent with powers of 2.

Concept / Approach:
Inspect transitions: 2 → 8 (×4), 8 → 16 (×2), 16 → 128 (×8). The multipliers themselves are 4, 2, 8 which are 2^2, 2^1, 2^3. A natural continuation is to apply the next increasing power 2^4 = 16 to 128.

Step-by-Step Solution:
Identify multiplier sequence as powers of 2: 2^2, 2^1, 2^3, 2^4 ... Compute next term: 128 × 16 = 2048. Check internal consistency: each jump uses a power of 2; the exponents visited (2,1,3,4) include a plausible step-up to 4 next.

Verification / Alternative check:
2048 is itself 2^11; the rapid growth matches the observed leap from 16 to 128 (×8).

Why Other Options Are Wrong:
2042/2046/2056: Not powers of 2 and not equal to 128 × 2^k for integer k; they break the power-of-two multiplier theme.

Common Pitfalls:
Expecting constant multipliers or trying to add instead of multiply, which cannot produce 128 from 16 without a large inconsistent jump.

Final Answer:
2048