Question

use the method of Gauss to find the sum.

2+4+6+...+300

is it 300(300+2)/2 = 45300

Answer 1

close, but incorrect

there are only 150 terms in the sequence 2,4,6,.. 300

so according to Gauss, it would be
150(2+300)/2
= 22650

Proof: long way
a = 2 , d = 2
t(n) = a+(n-1)d
300 = 2 + (n-1)2
300 = 2 + 2n - 2
n = 150

S(150) = (150/2)(4 + 149(2))
= 22650