### Video Transcript

Which of the following represents the sequence one, two, three, four, and so on?

In this question, we are given five possible graphs that represent the sequence given. The sequence has first term one, second term two, third term three, and fourth term four. This is an example of an arithmetic sequence as the difference between each term is constant. There is a common difference of one as each term is one larger than the previous term. We know that any arithmetic sequence will be represented on the 𝑥𝑦-coordinate plane by a linear or straight-line graph.

It is clear that option (A) matches these criteria. The four points have coordinates one, one; two, two; three, three; and four, four. This matches our sequence where the 𝑥-coordinate is the index or term number and the 𝑦-coordinates represent the terms in the sequence. We have a first term of one, a second term of two, a third term of three, and a fourth term of four. This means that graph (A) represents the sequence one, two, three, four, and so on.

We can check that the other four graphs are incorrect by looking at the coordinates or the shape of the graph. Graph (B) has points with coordinates one, one; three, two; four, three; and five, four. Apart from the first point, these do not match our sequence. And it is also clear that three of the points do not lie on the correct straight-line graph. Repeating this process for options (C) and (D), it is clear that none of the points lie on the correct graph. Whilst the first two points of graph (E) do match the sequence, the coordinates five, three and seven, four do not. Therefore, this is not the correct graph of the sequence. By ruling out the other options, we have confirmed that the graph that represents the sequence one, two, three, four is graph (A).