The 4th and 9th terms of an AP are in the ratio 2 : 3, and its 7th term is 26. Find the first term.

From $(a+3d)/(a+8d)=2/3$ we get $3a+9d=2a+16d$, so $a=7d$. Then $a_7=a+6d=13d=26$ gives $d=2$ and $a=14$. (Check: $a_4=20,a_9=30$, and 20 : 30 = 2 : 3.) The value 2 is the common difference and 20 is the 4th term, not the first term.