How do I graph the first six terms of a sequence if the first term is 3 and the common difference is 10?

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To graph the first six terms of a sequence where the first term (
a1) is 3 and the common difference (d) is 10, you will first need to identify the sequence itself. This type of sequence is known as an arithmetic sequence, which is defined by the formula:

an = a1 + (n – 1) * d

Here, n represents the term number. We can now calculate the first six terms:

  1. a1 = 3
  2. a2 = 3 + (2 – 1) * 10 = 3 + 10 = 13
  3. a3 = 3 + (3 – 1) * 10 = 3 + 20 = 23
  4. a4 = 3 + (4 – 1) * 10 = 3 + 30 = 33
  5. a5 = 3 + (5 – 1) * 10 = 3 + 40 = 43
  6. a6 = 3 + (6 – 1) * 10 = 3 + 50 = 53

So, the first six terms of the sequence are: 3, 13, 23, 33, 43, and 53.

Next, to graph these terms, you can use a simple Cartesian coordinate system where the x-axis represents the term number (n) and the y-axis represents the value of the term (an):

  • n = 1, a1 = 3
  • n = 2, a2 = 13
  • n = 3, a3 = 23
  • n = 4, a4 = 33
  • n = 5, a5 = 43
  • n = 6, a6 = 53

To plot the points on the graph:

  • Point (1, 3)
  • Point (2, 13)
  • Point (3, 23)
  • Point (4, 33)
  • Point (5, 43)
  • Point (6, 53)

Once you have plotted these points, you can draw a straight line connecting them, as the points will align perfectly due to the nature of an arithmetic sequence. This line represents the linear growth of the sequence over the specified terms.

Graphing this arithmetic sequence not only provides a visual representation of how the value of the terms increases but also highlights the consistent pattern of growth determined by the common difference of 10. You now have a clear way to visualize this sequence on a graph!

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