Mathematics

Question

use the approach in Gauss’s Problem to find the following sums of arithmetic sequences

 

a) 1 + 3 + 5 + 7 + ... + 2009

 

b) 6 + 12 + 18 + ... + 600

 

c) 1000 + 995 + 990 + ... + 5

Answer 1

a)

a_n = a₁ + (n - 1)d

2009 = 1 + 2n - 2

2009 = -1 + 2n

2010 = 2n

1005 = n

 

S₁₀₀₅ = (1005/2)(1 + 2009)

 

Can you solve for S₁₀₀₅?

 

b) and c) done the same way