Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 902: 16

$a_{14}=-\frac{17}{3}$

In an arithmetic sequence, first we have to find the common difference, which can be calculated as the difference of any two subsequent terms: $d=a_2-a_1=\frac{7}{3}-3=-\frac{2}{3}$ The n th term can be calculated as: $a_n=a_1+d\times(n-1)$ The 14th term is: $a_{14}=3+(-\frac{2}{3})\times(14-1)=-\frac{17}{3}$