Find the 5,550th term in the sequence

4 1/2, 5, 5 1/2, 6, 6 1/2

looks like an AS

with a = 4.5 and d= .5

term(5550)
= a + 5549d
= 4.5 + 5549(.5)
= ....

2779?

To find the 5,550th term in the sequence, let's analyze the given sequence first:

4 1/2, 5, 5 1/2, 6, 6 1/2

From the given sequence, we can observe that each term increases by 1/2. We also notice that the terms alternate between whole numbers and numbers with a half, such as 4 1/2 and 5 1/2.

Now, let's break down the sequence into two separate progressions:

1) The sequence of whole numbers: 4, 5, 6

2) The sequence of numbers with a half: 1/2, 1, 1 1/2, 2, 2 1/2

Both progressions have common differences of 1. To determine the pattern of the sequence, we need to find how many terms there are in each progression before reaching the desired term.

1) Whole numbers progression: Since each term increases by 1, we just need to subtract 4 (the first term) from the desired term number (5,550).

(5,550) - 4 = 5,546

So, there are 5,546 terms in the whole numbers progression before reaching the 5,550th term.

2) Numbers with a half progression: Since each term also increases by 1, we need to subtract 1/2 (the first term) from the desired term number.

(5,550) - 1/2 = 5,549 1/2

So, there are 5,549 1/2 terms in the numbers with a half progression before reaching the 5,550th term.

To find the overall pattern, we can observe that the whole numbers progress one term after the numbers with a half. So, the 5,550th term corresponds to the 5,550th term in the whole numbers progression.

Now, let's find the value of the 5,550th term in the whole numbers progression by adding the common difference, 1, to the first term, 4:

4 + 1 = 5

Therefore, the 5,550th term in the sequence is 5.