SOLUTION: in any six number string ie : 2-23-26-30-40- 49 the first number plus the sum of the difference between the numbers equal the last number ie 2+20+3+14+10+9= 49 PLEASE EXPLAIN

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Question 935631: in any six number string ie : 2-23-26-30-40- 49
the first number plus the sum of the difference between the numbers equal the last number ie 2+20+3+14+10+9= 49
PLEASE EXPLAIN
THANK YOU
JOHN

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the 6 number string:
a, b, c, d, e, f
-------------------
They say that:
(1) +a+%2B+%28+b-a+%29+%2B+%28+c-b+%29+%2B+%28+d-c+%29+%2B+%28+e-d+%29+%2B+%28+f-e+%29+=+f+
Rearrange this:
+%28a+-+a%29+%2B+%28b+-+b%29+%2B+%28c+-+c%29+%2B+%28d+-+d%29+%2B+%28e+-+e%29+%2B+f+=+f+
+5%2A0+%2B+f+=+f+
+f+=+f+
-------------
This proves it for any numbers
Suppose you had a combination of numbers
and letters:
2, b, 7, -8, e, -2
Just plug these values into (1)
(1) +a+%2B+%28+b-a+%29+%2B+%28+c-b+%29+%2B+%28+d-c+%29+%2B+%28+e-d+%29+%2B+%28+f-e+%29+=+f+
(1)
(1)
(1) +5%2A0+-+2+=+-2+
(1) +-2+=+-2+
OK