Question

20 PTS ,, MATH HELP PLEASE??

Find the first six terms of the sequence.

a1 = -7, an = 4 • an-1



Find an equation for the nth term of the sequence.

-1, -4, -16, -64, ...

Answer 1

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

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)`