Respuesta :

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]

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