32 KAN^A^ ACADEMY OF ^SCIENCE. 



CASE I. EVEN SERIES. 



Common difference of series, 4. 

 .... 16 9 4 1 1 4 " 9 16 25 36 

 .... -12 -8 -4 4 8 12 16 20 24 28 



.... 4 1 1 4 9 16 25 36 49 64 



Common difference, S. 

 ....86 25 16 9 4 1 1 4 9 16 

 .... -32 -24 -16-8 8 16 24 32 40 48 



4 1 1 4 9 16 25 36 49 64 81 100 121 144 



Common difference, 12. 



64 49 36 25 16 9 4 i 1 4 9 16 25 36 



-60 -48 -36 -24 -12 12 24 36 48 60 72 84 96 108 



4 1 1 4 9 16 25 36 49 64 81 100 121 144 



Common difference, 20. 



144 121 100 81 64 49 36 25 16 9 4 1 1 4 



-140 -120 -100 -80 -60 -40 -20 20 40 60 80 100 120 140 



4 1 1 4 9 16 25 36 49 64 81 100 121 144 



Common difference, 32. 



100 81 64 49 36 25 16 9 4 1 1 4 



-64 -32 32 64 96 128 160 192 224 256 288 320 



36 49 64 81 100 121 144 169 196 225 256 289 324 



Common difference, 60. 



400 361 324 289 256 225 196 109 144 121 100 81 



-300 -240 -180 -120 -60 60 120 180 240 300 360 



100 121 144 169 196 225 256 289 324 361 400 441 



Common difference, 100. 



900 841 784 729 676 625 576 529 484 441 400 361 



-500 -400 -300 -200 -100 100 200 300 400 500 600 



1 4 9 16 25 36 49 64 81 100 121 144 169 196 



Common difference, I4. 



49 36 25 16 9 4 1 1 4 9 16 25 36 49 



-49 -35 -21 -7 7 21 35 49 63 77 91 105 119 133 147 



1 4 9 16 25 36 49 64 81 100 121 144 169 196 



