Answer:
[tex]c_{5}[/tex] = - 12
Step-by-step explanation:
To find the 5 th term in the sequence, calculate the 3 rd and 4 th terms, that is
[tex]c_{3}[/tex] = - 2[tex]c_{2}[/tex] - [tex]c_{1}[/tex] - 1 ← substitute in values
= - 2(1) - 2 - 1 = - 2 - 2 - 1 = - 5
[tex]c_{4}[/tex] = - 2[tex]c_{3}[/tex] - [tex]c_{2}[/tex] - 1 ← substitute values
= - 2(- 5) - 1 - 1 = 10 - 1 - 1 = 8
[tex]c_{5}[/tex] = - 2[tex]c_{4}[/tex] - [tex]c_{3}[/tex] - 1 ← substitute values
= - 2(8) - (- 5) - 1 = - 16 + 5 - 1 = - 12