Sum of First 700 Odd Numbers

The below workout with step by step solution using easiest method, shows how to find the sum of first 700 odd numbers by applying arithmetic progression.
step 1 Input Parameters and values:
The number series 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 201, 203, 205, 207, 209, 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 233, 235, 237, 239, 241, 243, 245, 247, 249, 251, 253, 255, 257, 259, 261, 263, 265, 267, 269, 271, 273, 275, 277, 279, 281, 283, 285, 287, 289, 291, 293, 295, 297, 299, 301, 303, 305, 307, 309, 311, 313, 315, 317, 319, 321, 323, 325, 327, 329, 331, 333, 335, 337, 339, 341, 343, 345, 347, 349, 351, 353, 355, 357, 359, 361, 363, 365, 367, 369, 371, 373, 375, 377, 379, 381, 383, 385, 387, 389, 391, 393, 395, 397, 399, 401, 403, 405, 407, 409, 411, 413, 415, 417, 419, 421, 423, 425, 427, 429, 431, 433, 435, 437, 439, 441, 443, 445, 447, 449, 451, 453, 455, 457, 459, 461, 463, 465, 467, 469, 471, 473, 475, 477, 479, 481, 483, 485, 487, 489, 491, 493, 495, 497, 499, 501, 503, 505, 507, 509, 511, 513, 515, 517, 519, 521, 523, 525, 527, 529, 531, 533, 535, 537, 539, 541, 543, 545, 547, 549, 551, 553, 555, 557, 559, 561, 563, 565, 567, 569, 571, 573, 575, 577, 579, 581, 583, 585, 587, 589, 591, 593, 595, 597, 599, 601, 603, 605, 607, 609, 611, 613, 615, 617, 619, 621, 623, 625, 627, 629, 631, 633, 635, 637, 639, 641, 643, 645, 647, 649, 651, 653, 655, 657, 659, 661, 663, 665, 667, 669, 671, 673, 675, 677, 679, 681, 683, 685, 687, 689, 691, 693, 695, 697, 699, 701, 703, 705, 707, 709, 711, 713, 715, 717, 719, 721, 723, 725, 727, 729, 731, 733, 735, 737, 739, 741, 743, 745, 747, 749, 751, 753, 755, 757, 759, 761, 763, 765, 767, 769, 771, 773, 775, 777, 779, 781, 783, 785, 787, 789, 791, 793, 795, 797, 799, 801, 803, 805, 807, 809, 811, 813, 815, 817, 819, 821, 823, 825, 827, 829, 831, 833, 835, 837, 839, 841, 843, 845, 847, 849, 851, 853, 855, 857, 859, 861, 863, 865, 867, 869, 871, 873, 875, 877, 879, 881, 883, 885, 887, 889, 891, 893, 895, 897, 899, 901, 903, 905, 907, 909, 911, 913, 915, 917, 919, 921, 923, 925, 927, 929, 931, 933, 935, 937, 939, 941, 943, 945, 947, 949, 951, 953, 955, 957, 959, 961, 963, 965, 967, 969, 971, 973, 975, 977, 979, 981, 983, 985, 987, 989, 991, 993, 995, 997, 999, 1001, 1003, 1005, 1007, 1009, 1011, 1013, 1015, 1017, 1019, 1021, 1023, 1025, 1027, 1029, 1031, 1033, 1035, 1037, 1039, 1041, 1043, 1045, 1047, 1049, 1051, 1053, 1055, 1057, 1059, 1061, 1063, 1065, 1067, 1069, 1071, 1073, 1075, 1077, 1079, 1081, 1083, 1085, 1087, 1089, 1091, 1093, 1095, 1097, 1099, 1101, 1103, 1105, 1107, 1109, 1111, 1113, 1115, 1117, 1119, 1121, 1123, 1125, 1127, 1129, 1131, 1133, 1135, 1137, 1139, 1141, 1143, 1145, 1147, 1149, 1151, 1153, 1155, 1157, 1159, 1161, 1163, 1165, 1167, 1169, 1171, 1173, 1175, 1177, 1179, 1181, 1183, 1185, 1187, 1189, 1191, 1193, 1195, 1197, 1199, 1201, 1203, 1205, 1207, 1209, 1211, 1213, 1215, 1217, 1219, 1221, 1223, 1225, 1227, 1229, 1231, 1233, 1235, 1237, 1239, 1241, 1243, 1245, 1247, 1249, 1251, 1253, 1255, 1257, 1259, 1261, 1263, 1265, 1267, 1269, 1271, 1273, 1275, 1277, 1279, 1281, 1283, 1285, 1287, 1289, 1291, 1293, 1295, 1297, 1299, 1301, 1303, 1305, 1307, 1309, 1311, 1313, 1315, 1317, 1319, 1321, 1323, 1325, 1327, 1329, 1331, 1333, 1335, 1337, 1339, 1341, 1343, 1345, 1347, 1349, 1351, 1353, 1355, 1357, 1359, 1361, 1363, 1365, 1367, 1369, 1371, 1373, 1375, 1377, 1379, 1381, 1383, 1385, 1387, 1389, 1391, 1393, 1395, 1397, 1399, .
The first term a = 1
The common difference d = 2
Total number of terms n = 700

step 2 apply the input parameter values in the AP formula
Sum = n/2 x (a + T_n)
= 700/2 x (1 + )
= (700 x 1)/ 2
= 700/2
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35 + 37 + 39 + 41 + 43 + 45 + 47 + 49 + 51 + 53 + 55 + 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71 + 73 + 75 + 77 + 79 + 81 + 83 + 85 + 87 + 89 + 91 + 93 + 95 + 97 + 99 + 101 + 103 + 105 + 107 + 109 + 111 + 113 + 115 + 117 + 119 + 121 + 123 + 125 + 127 + 129 + 131 + 133 + 135 + 137 + 139 + 141 + 143 + 145 + 147 + 149 + 151 + 153 + 155 + 157 + 159 + 161 + 163 + 165 + 167 + 169 + 171 + 173 + 175 + 177 + 179 + 181 + 183 + 185 + 187 + 189 + 191 + 193 + 195 + 197 + 199 + 201 + 203 + 205 + 207 + 209 + 211 + 213 + 215 + 217 + 219 + 221 + 223 + 225 + 227 + 229 + 231 + 233 + 235 + 237 + 239 + 241 + 243 + 245 + 247 + 249 + 251 + 253 + 255 + 257 + 259 + 261 + 263 + 265 + 267 + 269 + 271 + 273 + 275 + 277 + 279 + 281 + 283 + 285 + 287 + 289 + 291 + 293 + 295 + 297 + 299 + 301 + 303 + 305 + 307 + 309 + 311 + 313 + 315 + 317 + 319 + 321 + 323 + 325 + 327 + 329 + 331 + 333 + 335 + 337 + 339 + 341 + 343 + 345 + 347 + 349 + 351 + 353 + 355 + 357 + 359 + 361 + 363 + 365 + 367 + 369 + 371 + 373 + 375 + 377 + 379 + 381 + 383 + 385 + 387 + 389 + 391 + 393 + 395 + 397 + 399 + 401 + 403 + 405 + 407 + 409 + 411 + 413 + 415 + 417 + 419 + 421 + 423 + 425 + 427 + 429 + 431 + 433 + 435 + 437 + 439 + 441 + 443 + 445 + 447 + 449 + 451 + 453 + 455 + 457 + 459 + 461 + 463 + 465 + 467 + 469 + 471 + 473 + 475 + 477 + 479 + 481 + 483 + 485 + 487 + 489 + 491 + 493 + 495 + 497 + 499 + 501 + 503 + 505 + 507 + 509 + 511 + 513 + 515 + 517 + 519 + 521 + 523 + 525 + 527 + 529 + 531 + 533 + 535 + 537 + 539 + 541 + 543 + 545 + 547 + 549 + 551 + 553 + 555 + 557 + 559 + 561 + 563 + 565 + 567 + 569 + 571 + 573 + 575 + 577 + 579 + 581 + 583 + 585 + 587 + 589 + 591 + 593 + 595 + 597 + 599 + 601 + 603 + 605 + 607 + 609 + 611 + 613 + 615 + 617 + 619 + 621 + 623 + 625 + 627 + 629 + 631 + 633 + 635 + 637 + 639 + 641 + 643 + 645 + 647 + 649 + 651 + 653 + 655 + 657 + 659 + 661 + 663 + 665 + 667 + 669 + 671 + 673 + 675 + 677 + 679 + 681 + 683 + 685 + 687 + 689 + 691 + 693 + 695 + 697 + 699 + 701 + 703 + 705 + 707 + 709 + 711 + 713 + 715 + 717 + 719 + 721 + 723 + 725 + 727 + 729 + 731 + 733 + 735 + 737 + 739 + 741 + 743 + 745 + 747 + 749 + 751 + 753 + 755 + 757 + 759 + 761 + 763 + 765 + 767 + 769 + 771 + 773 + 775 + 777 + 779 + 781 + 783 + 785 + 787 + 789 + 791 + 793 + 795 + 797 + 799 + 801 + 803 + 805 + 807 + 809 + 811 + 813 + 815 + 817 + 819 + 821 + 823 + 825 + 827 + 829 + 831 + 833 + 835 + 837 + 839 + 841 + 843 + 845 + 847 + 849 + 851 + 853 + 855 + 857 + 859 + 861 + 863 + 865 + 867 + 869 + 871 + 873 + 875 + 877 + 879 + 881 + 883 + 885 + 887 + 889 + 891 + 893 + 895 + 897 + 899 + 901 + 903 + 905 + 907 + 909 + 911 + 913 + 915 + 917 + 919 + 921 + 923 + 925 + 927 + 929 + 931 + 933 + 935 + 937 + 939 + 941 + 943 + 945 + 947 + 949 + 951 + 953 + 955 + 957 + 959 + 961 + 963 + 965 + 967 + 969 + 971 + 973 + 975 + 977 + 979 + 981 + 983 + 985 + 987 + 989 + 991 + 993 + 995 + 997 + 999 + 1001 + 1003 + 1005 + 1007 + 1009 + 1011 + 1013 + 1015 + 1017 + 1019 + 1021 + 1023 + 1025 + 1027 + 1029 + 1031 + 1033 + 1035 + 1037 + 1039 + 1041 + 1043 + 1045 + 1047 + 1049 + 1051 + 1053 + 1055 + 1057 + 1059 + 1061 + 1063 + 1065 + 1067 + 1069 + 1071 + 1073 + 1075 + 1077 + 1079 + 1081 + 1083 + 1085 + 1087 + 1089 + 1091 + 1093 + 1095 + 1097 + 1099 + 1101 + 1103 + 1105 + 1107 + 1109 + 1111 + 1113 + 1115 + 1117 + 1119 + 1121 + 1123 + 1125 + 1127 + 1129 + 1131 + 1133 + 1135 + 1137 + 1139 + 1141 + 1143 + 1145 + 1147 + 1149 + 1151 + 1153 + 1155 + 1157 + 1159 + 1161 + 1163 + 1165 + 1167 + 1169 + 1171 + 1173 + 1175 + 1177 + 1179 + 1181 + 1183 + 1185 + 1187 + 1189 + 1191 + 1193 + 1195 + 1197 + 1199 + 1201 + 1203 + 1205 + 1207 + 1209 + 1211 + 1213 + 1215 + 1217 + 1219 + 1221 + 1223 + 1225 + 1227 + 1229 + 1231 + 1233 + 1235 + 1237 + 1239 + 1241 + 1243 + 1245 + 1247 + 1249 + 1251 + 1253 + 1255 + 1257 + 1259 + 1261 + 1263 + 1265 + 1267 + 1269 + 1271 + 1273 + 1275 + 1277 + 1279 + 1281 + 1283 + 1285 + 1287 + 1289 + 1291 + 1293 + 1295 + 1297 + 1299 + 1301 + 1303 + 1305 + 1307 + 1309 + 1311 + 1313 + 1315 + 1317 + 1319 + 1321 + 1323 + 1325 + 1327 + 1329 + 1331 + 1333 + 1335 + 1337 + 1339 + 1341 + 1343 + 1345 + 1347 + 1349 + 1351 + 1353 + 1355 + 1357 + 1359 + 1361 + 1363 + 1365 + 1367 + 1369 + 1371 + 1373 + 1375 + 1377 + 1379 + 1381 + 1383 + 1385 + 1387 + 1389 + 1391 + 1393 + 1395 + 1397 + 1399 + =

Therefore,
is the sum of first 700 odd numbers.