SOLUTION: Please help me answer by finding the sum of the following sequence of numbers: 2+4+6+8+.......296+298+300 Thanks in advance

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Question 321468: Please help me answer by finding the sum of the following sequence of numbers:
2+4+6+8+.......296+298+300 Thanks in advance
Found 3 solutions by checkley77, scott8148, Edwin McCravy:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website!
Sum=n/2(a+L)=150/2(2+300)=75*302=22,650 ans.

Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website!
the 1st plus last is 302
the 2nd plus next to last is 302
the 3rd plus next to next to last is 302
___ getting the picture?

there are 150 such pairs (300 / 2)

so the sum of the sequence is ___ 302 * 150

Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!

Two methods: Method 1: The sum is twice the sum 1 + 2 + ... + 150, so there are 150 terms. Here is how to do it without using any formulas: Let S represent the sum. S = 2 + 4 + 6 + 8 + ... + 294 + 296 + 298 + 300 Under that write the sum of the 150 terms in descending order: S = 2 + 4 + 6 + 8 + ... + 294 + 296 + 298 + 300 S = 300 + 298 + 296 + 294 + ... + 8 + 6 + 4 + 2 Add them term by term: S = 2 + 4 + 6 + 8 + ... + 294 + 296 + 298 + 300 S = 300 + 298 + 296 + 294 + ... + 8 + 6 + 4 + 2 ------------------------------------------------------- 2S = 302 + 302 + 302 + 302 + ... + 302 + 302 + 302 + 302 Therefore since there are 150 terms, there are 150 302's on the right, so 2S = 150*302 2S = 45300 S = 22650 Method 2: Using formulas for an arithmetic series: , , Edwin