The first option is your answer.
Sigma notation is just a fancy way to shorten a sum of a series of numbers using a set equation. The "n =" tells you where to start in the sequence and the top number tells you where to stop.
Suppose
At the same time, we can write
Note that 
(just reverse the sum). Let's pair the first terms of 
and 
, and the second, and the third, and so on:
Now, each grouped term in the sum on the right side adds to 151. There are 52 grouped terms on that same side (because there are 50 numbers in the range of integers 51-100, plus 50 and 101), which menas
But , as we pointed out, so
Answer:
4x² -3y
Step-by-step explanation:
Answer:
he is an ordinary man because that is what the speaker is talking about
<span> To get an explicit formula, we need to find an expression which gives the n-th term without having to compute earlier terms in the sequence. Looking at the numbers, and from the recursive formula, we see that the sequence is built by subtracting n from the previous term. This is similar to the triangular number sequence 1,3,6,10,15,... which has the explicit formula a_n = n(n+1)/2. In our case we are subtracting n from the previous term, so we multiply by -1/2 instead of 1/2. However, we also need to add a constant term to reproduce the numbers of the sequence. We can write a_1 = -1(2)/2 + c = 8. Therefore, c = 9.
So the explict formula is:
a_n = -n(n+1)/2 + 9</span>
