In a sequence, each term, starting from the third, is the sum of the two immediately preceding terms. If the second term is 1 and the fifth term is 2005, what is the sixth term?
(a) 3002
(b) 3008
(c) 3010
(d) 4002
(e) 5004
The correct option is (b).

Let $x$ be the first term of the sequence. Since the second term is $1$, and from the third term onwards, each term is the sum of the two preceding ones, we have:

- the third term is $1+x$;
- the fourth term is $1+(1+x)=2+x$;
- the fifth term is $(1+x)+(2+x)=3+2x$;
- the sixth term is $(2+x)+(3+2x)=5+3x$.

Since the fifth term is 2005, we have $3+2x=2005$, from which $x=1001$. Therefore, the sixth term of the sequence is $5+3 \times 1001=3008$.