UpStudy Free Solution:

To count by hundreds from 6 up to 906, you would add 100 to 6 repeatedly. Here are the numbers:

1. 6

2. 106

3. 206

4. 306

5. 406

6. 506

7. 606

8. 706

9. 806

10. 906

So the sequence is: 6, 106, 206, 306, 406, 506, 606, 706, 806, 906.

Supplemental Knowledge

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. Here’s a closer look at arithmetic sequences:

1. Definition:

- An arithmetic sequence can be defined by its first term (\(a_ 1\)) and the common difference (\(d\)).

- The \(n\)-th term of an arithmetic sequence can be calculated using the formula:

\[a_ n = a_ 1 + ( n- 1) \cdot d\]

2. Example Sequence:

- Given the first term \(a_ 1 = 6\) and the common difference \(d = 100\), we can generate the terms of the sequence.

- For example, to find the 10th term (\(a_ { 10} \)):

\[a_ { 10} = 6 + ( 10- 1) \cdot 100 = 6 + 900 = 906\]

3. Properties:

- Arithmetic sequences are linear, meaning they graph as straight lines.

- The sum of an arithmetic series (the sum of the first \(n\) terms) can be calculated using:

\[S_ n = \frac { n} { 2} ( a_ 1 + a_ n) \]

- For our example, summing up to \(a_ { 10} \):

\[S_ { 10} = \frac { 10} { 2} ( 6 + 906) = 5 \cdot 912 = 4560\]

Mastering arithmetic sequences opens a whole world of mathematical discovery! At UpStudy, we make learning complex mathematical concepts such as this engaging and enjoyable. UpStudy offers comprehensive resources that cover everything from basic counting to advanced calculus - and everything in between!