Look at the sequence in this table
n 1 2 3 4 5 ...
An -1 1 3 5 7 ...
Which function represents the sequence?
A) an = an - 1 + 1
B) an = an - 1 + 2
C) an = 2an - 1 -1 ***
D) an = 2an -1 - 3
notice that the values of an increase by 2
so we need something like ?? = ?? + 2
there is only one such pattern and it is B
It should have been:
an = an-1 + 2, a1 = -1 , n>1
that last part must be included, or else the sequence has no start
I know I might be late to tell you this, but thank you so much!
To determine which function represents the given sequence, let's analyze the pattern in the table.
Looking at the values of An, we can see that each term is obtained by adding 2 to the previous term. For example, the first term is -1, and to get the second term, we add 2: -1 + 2 = 1. Similarly, we can continue this pattern to get subsequent terms.
Therefore, the correct answer would be:
C) an = 2an - 1 - 1
To determine the function that represents the sequence in the table, we need to analyze the pattern between the terms.
Looking at the table, we can observe that each term (An) is obtained by adding a specific amount to the previous term. Specifically, each term is obtained by adding 2 to the previous term.
Knowing this, we can now establish the relationship between the terms using a functional notation. Let's call the current term An and the previous term An-1.
Based on the pattern, we can write the function as follows:
An = An-1 + 2
Now, let's compare this functional representation with the given options:
A) an = an - 1 + 1 - The pattern in the table adds 2 to the previous term, not 1. Therefore, this option does not represent the given sequence.
B) an = an - 1 + 2 - This option matches our previously determined pattern. It represents the given sequence.
C) an = 2an - 1 - 1 - This option does not match the given pattern. In this option, the current term is multiplied by 2 and then subtracted by 1, which is not consistent with the table.
D) an = 2an - 1 - 3 - Similar to option C, this option does not match the given pattern. Here, the current term is multiplied by 2 and then subtracted by 3, which is not the same as adding 2.
Therefore, the correct function that represents the sequence in the table is:
An = An-1 + 2