In an AP with common difference d, the 14th term is 3. Write the 23rd term in terms of d.

Going from the 14th term to the 23rd term takes 23 - 14 = 9 steps, so $a_{23}=a_{14}+9d=3+9d$. Counting both endpoints gives the wrong 10 steps $(3+10d)$; $3+23d$ wrongly uses the term number itself; $3-9d$ moves backwards instead of forwards.