Answer:
[tex] a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2 [/tex]
Step-by-step explanation:
The first number in the sequence, [tex] a_1 [/tex], is -2.
Each number after that is the previous number multiplied by -2.
[tex] a_1 = -2 [/tex]
[tex] a_2 = a_1 \times (-2) = -2 \times (-2) = 4 [/tex]
[tex] a_3 = a_2 \times (-2) = 4 \times (-2) = -8 [/tex]
etc.
[tex] a_n = -2a_{n - 1} [/tex]
We start by stating that [tex] a_1 = -2 [/tex].
Now we need to show that for all n greater than or equal to 2, each number in the sequence is the previous number multiplied by -2.
[tex] a_n = -2a_{n - 1} [/tex]
Answer:
[tex] a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2 [/tex]
