Consider the sequence given by a plus 8 pattern: 2, 10, 18, 26, ...

Shae says that the formula for the sequence is f (n) = 8n + 2. Marcus tells Shae that she is wrong because the

formula for the sequence is f (n) = 8n - 6.

b. Find the 100th term in the sequence

The 100th term is 796

Step-by-step explanation:

To get this term, all you need to do is to put n = 100 in the formula of the sequence.

Now, you should probably wonder which formula is correct right?, well this is easy to get. We know the sequence cause it follows a pattern of 8, so let's try some values of n from 1 to 4, to get those numbers with the first formula:

n = 1,2,3,4

f (1) = 8 (1) + 2 = 10

f (2) = 8 (2) + 2 = 18

f (3) = 8 (3) + 2 = 26

As you can see, with the first formula, the first term is 10, and not 2. The only way to get 2 with n = 1 is with the second formula:

f (1) = 8 (1) - 6 = 2

f (2) = 8 (2) - 6 = 10

f (3) = 8 (3) - 6 = 18

f (4) = 8 (4) - 6 = 26

With n = 1, the second formula was better and correct.

The first formula could be right only beggining with n = 0. Here is the proof:

f (0) = 8 (0) + 2 = 2

Now that we know that the second formula is the correct one using n = 1, let's calculate the 100th, using n = 100

f (100) = 8 (100) - 6 = 800 - 6 = 794