Find the sum.
-2 + 4 + 6 + ... + 1,298
A)421,850
B)421,201
C)420,552
D)422,500

Question

Quizplus · Accepted Answer

We can use the formula for the sum of an arithmetic series: 
S = (n/2)(a + l) 
where S is the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, a = 2, l = 1, and we need to find n. The common difference is 2, so to get from 2 to 1, we need to subtract 1 from the last even number, which is 1,298.

1,298 - 2 = 1,296 
1,296/2 = 648

So there are 648 terms in the sequence. Now we can plug in the values:

S = (648/2)(2 + 1) 
S = 324(3) 
S = 972

Therefore, the sum of the sequence is 972. However, none of the answer choices match this. We made an error in our sequence: the sequence should look like this:

2 + 4 + 6 + ... + 1,296 + 1,298

So we need to add the last two terms:

1,296 + 1,298 = 2,594

Now we can use the formula again:

1. There are 649 terms in the sequence.
2. The sum is (649/2)(2 + 1,298) = 421,850.

Therefore, the answer is A) 421,850.

Find the Sum. -2 + 4 + 6 + ... + 1,298