Answer:
Option A.
Step-by-step explanation:
The given sequence is
24, 30, 36, 42, 48, ...
It is an AP. Here,
First term = 24
Common difference = 30-24 = 6
The given explicit formula for nth term is
where, 
is first term, d is common difference.
Substitute 
in the above formula.
The 500th term of the sequence is 3018.
Therefore, the correct option is A.
Answer:
B. 1,900
Step-by-step explanation:
Answer:
7/16.
Step-by-step explanation:
The first triangle has no shading.
The second triangle has 1/4 shaded.
The third has 3/9.
The fourth has 6/16.
Based on this pattern, we can assume that the number of small triangles in each triangle are going to be squared of numbers, since the first had 1, the second 4, the third 9, the fourth 16. So, the 8th triangle would have 8^2 small triangles, or 64 triangles in total.
The first triangle has no shaded triangles. The second has 1. The third has 3. The fourth has 6. If you study the pattern, the second triangle has 1 more than the previous, the third has 2 more, the fourth has three more. And so, the fifth triangle would have 6 + 4 = 10 triangles, the sixth would have 10 + 5 = 15 triangles, the seventh would have 15 + 6 = 21 triangles, and the eighth would have 21 + 7 = 28 shaded triangles.
So, the fraction of shaded triangles would be 28 / 64 = 14 / 32 = 7 / 16.
Hope this helps!
