If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th term 2 ?

[BTGModeratorVI]

If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th term 2 ?

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

Answer: E
Source: Official Guide

[Brent@GMATPrepNow]

If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th term 2 ?

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

Answer: E
Source: Official Guide

Given: term1 = 0 and term2 = 1

Target question: Does term5 equal 2?
Once we scan the two statements, we can probably jump straight to
.
.
.
Statements 1 and 2 combined
There are several possible sequences that satisfy BOTH statements. Here are two:
Case a: {0, 1, 2, 0, 2,...}. In this case, the answer to the target question is YES, term5 IS 2
Case b: {0, 1, 2, 0, 0,...}. In this case, the answer to the target question is NO, term5 is NOT 2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

[swerve]

If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th term 2 ?

(1) Each odd-numbered term is either 0 or 2.
(2) The 3rd term is 2.

Answer: E
Source: Official Guide

From the question stem, we have first term \(= 0, 2\)nd term\(=1\).

Statement 1 clearly insufficient. \(\Large{\color{red}\chi}\)

Statement 2: the third term is \(2\). We now have
\(0,1,2,\)

I see a pattern here. From the second term onward, each term is preceding term\(+1\).

What am I missing?