Like if the number is 4,359
You write 4 times 1,000+ 3times 100+ 5times 10+ 9 times 1
I mean... in order to try each one you need to try it atleast once so.. 1 might be your answer
<h3>
Answer: Choice A</h3>
What we do is simply replace every n with k+1. So (3n)^2 turns into (3(k+1))^2
We see that only choice A has the correct term mentioned on the left hand side, so this must be the answer.
The right hand side is treated the same way. We plug in n = k+1. Your teacher did a bit of algebraic manipulation to get what is shown for choice A.
For a better understanding of the solution provided here please go through the diagram in the file that has been attached.
As can be clearly seen from the question and the graph, the area is bounded by a straight line
which passes through the origin, the y axis and the horizontal line
.
As we can see from the graph, this is a right triangle. To find the point of intersection of the horizontal line y=6 and the line
, we will have to equate the two as:

Therefore, 
Thus, 
Hence the point of intersection is (12,6) which is depicted on the graph too.
As this is a case of a simple right triangle, the area of the bounded region will thus be:

Let the base be the y=6 line whose length is 12 and let height be the y axis whose length is 6, thus, the area will be:
squared units.