Question

Write a recursive formula for the sequence -2,4,-8, 16, ...

Answer 1

Answer:

$a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2$

Step-by-step explanation:

The first number in the sequence, $a_1$, is -2.

Each number after that is the previous number multiplied by -2.

$a_1 = -2$

$a_2 = a_1 \times (-2) = -2 \times (-2) = 4$

$a_3 = a_2 \times (-2) = 4 \times (-2) = -8$

etc.

$a_n = -2a_{n - 1}$

We start by stating that $a_1 = -2$.

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.

$a_n = -2a_{n - 1}$

Answer:

$a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2$