#### Answer

Converges to $-4$

#### Work Step by Step

$a_n = \frac{1}{4}a_{n-1}-3$; $a_0 = 1$
*Decimals are approximations
$a_0 = 1$
$a_1 = -2.75$
$a_2 = -3.6875$
$a_3 = -3.92188$
$a_4 = -3.98047$
$a_5 = -3.99512$
$a_6 = -3.99878$
$a_7 = -3.99969$
$a_8 = -3.99992$
$a_9 = -3.99998$
$a_{10} = -4.0$
The terms of the sequence seems to be approaching $-4$