Question

Each new triangle shown below has one more dot per side than the previous triangle. What is the total number of dots on the 200th triangle of this sequence? Answer:

Answer 1

The total number of dots on the 200th triangle is 603

Explanation:

Please check the attachment for the diagram of the triangular dots that completes the question

From the diagram, we can see that the first triangle has 6 total dots, second has 9 total dots, third has 12 total dots;

This shows a arithmetic progression pattern of the triangles where we have our first term being 6, with our common difference being the number of dots increment on all sides as we progress which is 3

Now we want to calculate for the 200th triangle

Mathematically, the nth term of an arithmetic sequence is given as;

Tn = a + (n-1)d

where a = 6 , d = 3 and n = 200

Substituting these values in the equation above, we have

Tn = 6 + (200-1)3

Tn = 6 + 199(3)

Tn = 6 + 597

Tn = 603