Answer:
The first five terms for given recursive formula are -1, 2, 8, 20, 44.
Step-by-step explanation:
Given:
[tex]a_1 = -1[/tex]
The recursive formula given is;
[tex]a_n=2(a_{n-1})+4[/tex]
Now we will find the first five terms using above formula.
We know the first term hence we find rest of the term.
when n=2;
[tex]a_2 = 2(a_{2-1})+4\\a_2=2(a_1)+4\\a_2=2\times-1+4\\a_2= -2+4\\a_2=2[/tex]
when n=3;
[tex]a_3 = 2(a_{3-1})+4\\a_3=2(a_2)+4\\a_3=2\times 2+4\\a_3= 4+4\\a_3=8[/tex]
when n=4;
[tex]a_4 = 2(a_{4-1})+4\\a_4=2(a_3)+4\\a_4=2\times 8+4\\a_4= 16+4\\a_4=20[/tex]
when n=5;
[tex]a_5 = 2(a_{5-1})+4\\a_5=2(a_4)+4\\a_5=2\times 20+4\\a_5= 40+4\\a_5=44[/tex]
Hence the first five terms for given recursive formula is -1, 2, 8, 20, 44.
