Question

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

Answer 1

The 100th term is 796

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