The below workout with step by step solution using easiest method, shows how to find the sum of first 140 even numbers by applying arithmetic progression.
step 1 Input Parameters and values:
The number series 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 252, 254, 256, 258, 260, 262, 264, 266, 268, 270, 272, 274, 276, 278, 280, .
The first term a = 2
The common difference d = 2
Total number of terms n = 140
step 2 apply the input parameter values in the AP formula
Sum = n/2 x (a + Tn)
= 140/2 x (2 + )
= (140 x 2)/ 2
= 280/2
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 + 56 + 58 + 60 + 62 + 64 + 66 + 68 + 70 + 72 + 74 + 76 + 78 + 80 + 82 + 84 + 86 + 88 + 90 + 92 + 94 + 96 + 98 + 100 + 102 + 104 + 106 + 108 + 110 + 112 + 114 + 116 + 118 + 120 + 122 + 124 + 126 + 128 + 130 + 132 + 134 + 136 + 138 + 140 + 142 + 144 + 146 + 148 + 150 + 152 + 154 + 156 + 158 + 160 + 162 + 164 + 166 + 168 + 170 + 172 + 174 + 176 + 178 + 180 + 182 + 184 + 186 + 188 + 190 + 192 + 194 + 196 + 198 + 200 + 202 + 204 + 206 + 208 + 210 + 212 + 214 + 216 + 218 + 220 + 222 + 224 + 226 + 228 + 230 + 232 + 234 + 236 + 238 + 240 + 242 + 244 + 246 + 248 + 250 + 252 + 254 + 256 + 258 + 260 + 262 + 264 + 266 + 268 + 270 + 272 + 274 + 276 + 278 + 280 + =
Therefore,
is the sum of first 140 even numbers.