[tex]a_n_+_1=-4a_n_+_2[/tex]
dividing both sides by -4, we get:
[tex]a_n_+_2=- \frac{a_n_+_1}{4} [/tex]
this means, each term is its previous term divided by -4.
now we can construct the sequence as follows:
[tex]a_1=2[/tex]
[tex]a_2=- \frac{a_1}{4}= - \frac{2}{4}= -\frac{1}{2} [/tex]
[tex]a_3=- \frac{a_2}{4} =- \frac{ \frac{1}{2} }{4}=- \frac{1}{8} [/tex]
[tex]a_4=- \frac{a_3}{4}=- \frac{ \frac{1}{8} }{4}=- \frac{1}{32} [/tex]
Answer: the last term is -1/32
