Answer:
a₁₅ = - [tex]\frac{31}{6}[/tex]
Step-by-step explanation:
There is a common difference between consecutive terms, that is
- [tex]\frac{5}{6}[/tex] - (- [tex]\frac{1}{2}[/tex] ) = - [tex]\frac{7}{6}[/tex] - (- [tex]\frac{5}{6}[/tex] ) = - [tex]\frac{1}{3}[/tex]
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - [tex]\frac{1}{2}[/tex] and d = - [tex]\frac{1}{3}[/tex] , then
a₁₅ = - [tex]\frac{1}{2}[/tex] + (14 × - [tex]\frac{1}{3}[/tex] = - [tex]\frac{1}{2}[/tex] - [tex]\frac{14}{3}[/tex] = - [tex]\frac{31}{6}[/tex]
