Question

n an
1 2
2 3
3 5
4 9
5 17

Look at the sequence in the table. Which recursive formula represents the sequence shown?
A) an = an-1 + 1
B) an = 3an-1 - 3
C) an = 2an-1 - 1
D) an = an-1 + 8

Answer 1

Answer:

$C)\ a_n=2a_{n-1}-1$

Explanation:

You can try the choices to see which one works. The differences between an values double each time. They have the sequence 1, 2, 4, 8. So, you know that choices A) and D) do not work. They show the difference to be constant at 1 or 8. Since the differences are multiplied by 2, C) is a reasonable choice. Trying that, we find it describes the sequence perfectly:

a2 = 2·2 -1 = 3

a3 = 2·3 -1 = 5

a4 = 2·5 -1 = 9

a5 = 2·9 -1 = 17

___

Trying choice B on the last term, we have

... a5 = 3·a4 -3 = 3·9 -3 = 24 ≠ 17