Answer:
The total number of dots on the 200th triangle is 603
Step-by-step 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
