Arithmetic Series

Question

Find 3-5+7-9+11-13+15-... to 80 terms. 

Answer 1

3-5+7-9+11-13+15-17+19-21...

find the sum to 80 terms

break this up into two parts

3+7+11+15+19....  (there will be 40 numbers )

-5-9-13-17-21...      (there will be 40 numbers )

add the first numbers in each sequence to get -2

add the second numbers in each sequence to get -2

add the third numbers in each sequence to get -2

keep doing this

 there will be 40 sums, each of which will be -2

40*(-2)=-80 for the sum

Answer 2

This is 2 arithmetic series Series 1: 3+7+11+ ... 40 terms, d = 4 Series 2: -5-9-13-... 40 terms, d = -4 series 1: a40 = 3+39(4)=159 series 2: a40 = -5+39(-4)= -161 sum series 1: (40/2)(3+159) = 3240 sum series 2: (40/2)(-5-161) = -3320 sum: 3240-3320 = -80