Question

Look at the sequence in the table. Which recursive formula represents the sequence shown? A

Answer 1

Answer:

B) $a_n=2a_{n-1}+1$

Step-by-step explanation:

To find this recursive formula, we need to look at the relationship between each term in the sequence.

When looking at n=1 and n=2, we can see that we have 5 and 11.

We have to find a pattern between each term in the sequence. If we double 5, which is the previous term, and add 1, we get 11.

Lets see if this works for the next term, 23

First, lets double 11 = 22

Now add 22+1=23. We got the right term. Lets test it again

23*2=46

46+1=47

And now the last term

47*2=94

96+1=95

As you can see doubling the previous term and adding 1 works for all of these terms.

when written as a recursive formula, it would be $a_n=2a_{n-1}+1$, which is B