Question

20 PTS ,, MATH HELP PLEASE??

Answer 1

Answer:

$Q1.\\\{-7,\ -28,\ -112,\ -448,\ -1792,\ -7168\}\\\\Q2.\\a_n=-4^{n-1}$

Step-by-step explanation:

$Q1.\\\\a_1=-7\\a_n=4a_{n-1}\\\\\text{Put n = 2, n = 3, ..., n = 6 to}\ a_n:\\\\a_2=4a_{2-1}=4a_1\to a_2=4(-7)=-28\\\\a_3=4a_{3-1}=4a_2\to a_3=4(-28)=-112\\\\a_4=4a_4-1}=4a_3\to a_4=4(-112)=-448\\\\a_5=4a_{5-1}=4a_4\to a_5=4(-448)=-1792\\\\a_6=4a_{6-1}=4a_5\to a_6=4(-1792)=-7168$

$Q2.\\\\-1,\ -4,\ -16,\ -64,\ ...\\\\a_1=-1=-4^0=-4^{1-1}\\a_2=-4=-4^1=-4^{2-1}\\a_3=-16=-4^2=-4^{3-1}\\a_4=-64=-4^3=-4^{4-1}\\\vdots\\a_n=-4^{n-1}$