In an AP the 12th term is twice its 5th term, and the common difference is 3. Find the first term.

$a_{12}=a+11\times 3=a+33$ and $a_5=a+4\times 3=a+12$. From $a+33=2(a+12)$ we get $a+33=2a+24$, so $a=9$. (Check: $a_5=21$ and $a_{12}=42=2\times 21$.) Using 12d and 5d instead of 11d and 4d gives 6; 21 is the 5th term, not the first; 3 is the common difference itself.