Answer:
[tex]\bold{a_{13}=52}[/tex]
Step-by-step explanation:
[tex]d=a_4-a_3=a_3-a_2\\\\a_3-a_2=a_4-a_3\\\\2a_3=a_2+a_4\\\\2a_3=13+7\\\\2a_3=20\\\\a_3=10\\\\d=10-13=-3\\\\\\a_2=a_1+d\quad\implies\quad a_1=a_2-d=13-(-3)=16\\\\a_n=a_1+d(n-1)\\\\a_{13}=16+(-3)(13-1)=16+36=52[/tex]
