college algebra word problem

Question

Express the arithmetic sum using summation notation.

5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50

Answer 1

factor out 5 to get

5(1+2+3+4+5+6+7+8+9+10)

the sum of 1 through 10 is 10(11)/2 = 55

multiply 55 x 5 = 275

10(11)/2 comes from Gauss' formula sum of 1 through n = n(n+1)/2

Gauss was a precious child, a math genius. When he was about 3 or so years old, his math teacher tried to keep him busy for a while, and asked him to calculate all integers 1 to 100. Gauss immediately gave the answer 5050. He had paired up 1 with 100, 2 with 99, 3 with 98 etc. to get 50 pairs of numbers that summed to 101. 50 times 101 = 5050. Thus began "Gauss' formula" for arithmetic sequences