1. **State the problem:** We are given a recursive sequence defined by $a_1 = 5$ and $a_n = -2a_{n-1}$ for $n \geq 2$. We need to find the value of $a_6$. 2. **Understand the formula:** The sequence is defined recursively, meaning each term depends on the previous term multiplied by $-2$. 3. **Calculate terms step-by-step:** - $a_1 = 5$ - $a_2 = -2 \times a_1 = -2 \times 5 = -10$ - $a_3 = -2 \times a_2 = -2 \times (-10) = 20$ - $a_4 = -2 \times a_3 = -2 \times 20 = -40$ - $a_5 = -2 \times a_4 = -2 \times (-40) = 80$ - $a_6 = -2 \times a_5 = -2 \times 80 = -160$ 4. **Final answer:** $$a_6 = -160$$ This means the sixth term of the sequence is $-160$.