Question

Which recursive sequence would produce the sequence 6,−13,25,…?

A) ​ a ₙ−1​ +7
B) a _n−1 −6
C) a_ n−1​ −1
D) a_ n =2a n−1 −7

Answer 1

The recursive sequence that would produce the sequence 6, -13, 25, ... is given by an = 2an-1 - 7.

Step-by-step explanation:

The recursive sequence that would produce the sequence 6, -13, 25, ... is given by option D) an = 2an-1 - 7.

To find each term in the sequence, we multiply the previous term by 2 and then subtract 7. Let's apply this formula step-by-step to verify:

1. a1 = 2(6) - 7 = 5
2. a2 = 2(5) - 7 = -7
3. a3 = 2(-7) - 7 = -13
4. a4 = 2(-13) - 7 = 25

Therefore, the recursive sequence that would produce the sequence 6, -13, 25, ... is given by an = 2an-1 - 7.