Sum of First 800 Even Numbers

The below workout with step by step solution using easiest method, shows how to find the sum of first 800 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, 282, 284, 286, 288, 290, 292, 294, 296, 298, 300, 302, 304, 306, 308, 310, 312, 314, 316, 318, 320, 322, 324, 326, 328, 330, 332, 334, 336, 338, 340, 342, 344, 346, 348, 350, 352, 354, 356, 358, 360, 362, 364, 366, 368, 370, 372, 374, 376, 378, 380, 382, 384, 386, 388, 390, 392, 394, 396, 398, 400, 402, 404, 406, 408, 410, 412, 414, 416, 418, 420, 422, 424, 426, 428, 430, 432, 434, 436, 438, 440, 442, 444, 446, 448, 450, 452, 454, 456, 458, 460, 462, 464, 466, 468, 470, 472, 474, 476, 478, 480, 482, 484, 486, 488, 490, 492, 494, 496, 498, 500, 502, 504, 506, 508, 510, 512, 514, 516, 518, 520, 522, 524, 526, 528, 530, 532, 534, 536, 538, 540, 542, 544, 546, 548, 550, 552, 554, 556, 558, 560, 562, 564, 566, 568, 570, 572, 574, 576, 578, 580, 582, 584, 586, 588, 590, 592, 594, 596, 598, 600, 602, 604, 606, 608, 610, 612, 614, 616, 618, 620, 622, 624, 626, 628, 630, 632, 634, 636, 638, 640, 642, 644, 646, 648, 650, 652, 654, 656, 658, 660, 662, 664, 666, 668, 670, 672, 674, 676, 678, 680, 682, 684, 686, 688, 690, 692, 694, 696, 698, 700, 702, 704, 706, 708, 710, 712, 714, 716, 718, 720, 722, 724, 726, 728, 730, 732, 734, 736, 738, 740, 742, 744, 746, 748, 750, 752, 754, 756, 758, 760, 762, 764, 766, 768, 770, 772, 774, 776, 778, 780, 782, 784, 786, 788, 790, 792, 794, 796, 798, 800, 802, 804, 806, 808, 810, 812, 814, 816, 818, 820, 822, 824, 826, 828, 830, 832, 834, 836, 838, 840, 842, 844, 846, 848, 850, 852, 854, 856, 858, 860, 862, 864, 866, 868, 870, 872, 874, 876, 878, 880, 882, 884, 886, 888, 890, 892, 894, 896, 898, 900, 902, 904, 906, 908, 910, 912, 914, 916, 918, 920, 922, 924, 926, 928, 930, 932, 934, 936, 938, 940, 942, 944, 946, 948, 950, 952, 954, 956, 958, 960, 962, 964, 966, 968, 970, 972, 974, 976, 978, 980, 982, 984, 986, 988, 990, 992, 994, 996, 998, 1000, 1002, 1004, 1006, 1008, 1010, 1012, 1014, 1016, 1018, 1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038, 1040, 1042, 1044, 1046, 1048, 1050, 1052, 1054, 1056, 1058, 1060, 1062, 1064, 1066, 1068, 1070, 1072, 1074, 1076, 1078, 1080, 1082, 1084, 1086, 1088, 1090, 1092, 1094, 1096, 1098, 1100, 1102, 1104, 1106, 1108, 1110, 1112, 1114, 1116, 1118, 1120, 1122, 1124, 1126, 1128, 1130, 1132, 1134, 1136, 1138, 1140, 1142, 1144, 1146, 1148, 1150, 1152, 1154, 1156, 1158, 1160, 1162, 1164, 1166, 1168, 1170, 1172, 1174, 1176, 1178, 1180, 1182, 1184, 1186, 1188, 1190, 1192, 1194, 1196, 1198, 1200, 1202, 1204, 1206, 1208, 1210, 1212, 1214, 1216, 1218, 1220, 1222, 1224, 1226, 1228, 1230, 1232, 1234, 1236, 1238, 1240, 1242, 1244, 1246, 1248, 1250, 1252, 1254, 1256, 1258, 1260, 1262, 1264, 1266, 1268, 1270, 1272, 1274, 1276, 1278, 1280, 1282, 1284, 1286, 1288, 1290, 1292, 1294, 1296, 1298, 1300, 1302, 1304, 1306, 1308, 1310, 1312, 1314, 1316, 1318, 1320, 1322, 1324, 1326, 1328, 1330, 1332, 1334, 1336, 1338, 1340, 1342, 1344, 1346, 1348, 1350, 1352, 1354, 1356, 1358, 1360, 1362, 1364, 1366, 1368, 1370, 1372, 1374, 1376, 1378, 1380, 1382, 1384, 1386, 1388, 1390, 1392, 1394, 1396, 1398, 1400, 1402, 1404, 1406, 1408, 1410, 1412, 1414, 1416, 1418, 1420, 1422, 1424, 1426, 1428, 1430, 1432, 1434, 1436, 1438, 1440, 1442, 1444, 1446, 1448, 1450, 1452, 1454, 1456, 1458, 1460, 1462, 1464, 1466, 1468, 1470, 1472, 1474, 1476, 1478, 1480, 1482, 1484, 1486, 1488, 1490, 1492, 1494, 1496, 1498, 1500, 1502, 1504, 1506, 1508, 1510, 1512, 1514, 1516, 1518, 1520, 1522, 1524, 1526, 1528, 1530, 1532, 1534, 1536, 1538, 1540, 1542, 1544, 1546, 1548, 1550, 1552, 1554, 1556, 1558, 1560, 1562, 1564, 1566, 1568, 1570, 1572, 1574, 1576, 1578, 1580, 1582, 1584, 1586, 1588, 1590, 1592, 1594, 1596, 1598, 1600, .
The first term a = 2
The common difference d = 2
Total number of terms n = 800

step 2 apply the input parameter values in the AP formula
Sum = n/2 x (a + T_n)
= 800/2 x (2 + )
= (800 x 2)/ 2
= 1600/2
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 + 282 + 284 + 286 + 288 + 290 + 292 + 294 + 296 + 298 + 300 + 302 + 304 + 306 + 308 + 310 + 312 + 314 + 316 + 318 + 320 + 322 + 324 + 326 + 328 + 330 + 332 + 334 + 336 + 338 + 340 + 342 + 344 + 346 + 348 + 350 + 352 + 354 + 356 + 358 + 360 + 362 + 364 + 366 + 368 + 370 + 372 + 374 + 376 + 378 + 380 + 382 + 384 + 386 + 388 + 390 + 392 + 394 + 396 + 398 + 400 + 402 + 404 + 406 + 408 + 410 + 412 + 414 + 416 + 418 + 420 + 422 + 424 + 426 + 428 + 430 + 432 + 434 + 436 + 438 + 440 + 442 + 444 + 446 + 448 + 450 + 452 + 454 + 456 + 458 + 460 + 462 + 464 + 466 + 468 + 470 + 472 + 474 + 476 + 478 + 480 + 482 + 484 + 486 + 488 + 490 + 492 + 494 + 496 + 498 + 500 + 502 + 504 + 506 + 508 + 510 + 512 + 514 + 516 + 518 + 520 + 522 + 524 + 526 + 528 + 530 + 532 + 534 + 536 + 538 + 540 + 542 + 544 + 546 + 548 + 550 + 552 + 554 + 556 + 558 + 560 + 562 + 564 + 566 + 568 + 570 + 572 + 574 + 576 + 578 + 580 + 582 + 584 + 586 + 588 + 590 + 592 + 594 + 596 + 598 + 600 + 602 + 604 + 606 + 608 + 610 + 612 + 614 + 616 + 618 + 620 + 622 + 624 + 626 + 628 + 630 + 632 + 634 + 636 + 638 + 640 + 642 + 644 + 646 + 648 + 650 + 652 + 654 + 656 + 658 + 660 + 662 + 664 + 666 + 668 + 670 + 672 + 674 + 676 + 678 + 680 + 682 + 684 + 686 + 688 + 690 + 692 + 694 + 696 + 698 + 700 + 702 + 704 + 706 + 708 + 710 + 712 + 714 + 716 + 718 + 720 + 722 + 724 + 726 + 728 + 730 + 732 + 734 + 736 + 738 + 740 + 742 + 744 + 746 + 748 + 750 + 752 + 754 + 756 + 758 + 760 + 762 + 764 + 766 + 768 + 770 + 772 + 774 + 776 + 778 + 780 + 782 + 784 + 786 + 788 + 790 + 792 + 794 + 796 + 798 + 800 + 802 + 804 + 806 + 808 + 810 + 812 + 814 + 816 + 818 + 820 + 822 + 824 + 826 + 828 + 830 + 832 + 834 + 836 + 838 + 840 + 842 + 844 + 846 + 848 + 850 + 852 + 854 + 856 + 858 + 860 + 862 + 864 + 866 + 868 + 870 + 872 + 874 + 876 + 878 + 880 + 882 + 884 + 886 + 888 + 890 + 892 + 894 + 896 + 898 + 900 + 902 + 904 + 906 + 908 + 910 + 912 + 914 + 916 + 918 + 920 + 922 + 924 + 926 + 928 + 930 + 932 + 934 + 936 + 938 + 940 + 942 + 944 + 946 + 948 + 950 + 952 + 954 + 956 + 958 + 960 + 962 + 964 + 966 + 968 + 970 + 972 + 974 + 976 + 978 + 980 + 982 + 984 + 986 + 988 + 990 + 992 + 994 + 996 + 998 + 1000 + 1002 + 1004 + 1006 + 1008 + 1010 + 1012 + 1014 + 1016 + 1018 + 1020 + 1022 + 1024 + 1026 + 1028 + 1030 + 1032 + 1034 + 1036 + 1038 + 1040 + 1042 + 1044 + 1046 + 1048 + 1050 + 1052 + 1054 + 1056 + 1058 + 1060 + 1062 + 1064 + 1066 + 1068 + 1070 + 1072 + 1074 + 1076 + 1078 + 1080 + 1082 + 1084 + 1086 + 1088 + 1090 + 1092 + 1094 + 1096 + 1098 + 1100 + 1102 + 1104 + 1106 + 1108 + 1110 + 1112 + 1114 + 1116 + 1118 + 1120 + 1122 + 1124 + 1126 + 1128 + 1130 + 1132 + 1134 + 1136 + 1138 + 1140 + 1142 + 1144 + 1146 + 1148 + 1150 + 1152 + 1154 + 1156 + 1158 + 1160 + 1162 + 1164 + 1166 + 1168 + 1170 + 1172 + 1174 + 1176 + 1178 + 1180 + 1182 + 1184 + 1186 + 1188 + 1190 + 1192 + 1194 + 1196 + 1198 + 1200 + 1202 + 1204 + 1206 + 1208 + 1210 + 1212 + 1214 + 1216 + 1218 + 1220 + 1222 + 1224 + 1226 + 1228 + 1230 + 1232 + 1234 + 1236 + 1238 + 1240 + 1242 + 1244 + 1246 + 1248 + 1250 + 1252 + 1254 + 1256 + 1258 + 1260 + 1262 + 1264 + 1266 + 1268 + 1270 + 1272 + 1274 + 1276 + 1278 + 1280 + 1282 + 1284 + 1286 + 1288 + 1290 + 1292 + 1294 + 1296 + 1298 + 1300 + 1302 + 1304 + 1306 + 1308 + 1310 + 1312 + 1314 + 1316 + 1318 + 1320 + 1322 + 1324 + 1326 + 1328 + 1330 + 1332 + 1334 + 1336 + 1338 + 1340 + 1342 + 1344 + 1346 + 1348 + 1350 + 1352 + 1354 + 1356 + 1358 + 1360 + 1362 + 1364 + 1366 + 1368 + 1370 + 1372 + 1374 + 1376 + 1378 + 1380 + 1382 + 1384 + 1386 + 1388 + 1390 + 1392 + 1394 + 1396 + 1398 + 1400 + 1402 + 1404 + 1406 + 1408 + 1410 + 1412 + 1414 + 1416 + 1418 + 1420 + 1422 + 1424 + 1426 + 1428 + 1430 + 1432 + 1434 + 1436 + 1438 + 1440 + 1442 + 1444 + 1446 + 1448 + 1450 + 1452 + 1454 + 1456 + 1458 + 1460 + 1462 + 1464 + 1466 + 1468 + 1470 + 1472 + 1474 + 1476 + 1478 + 1480 + 1482 + 1484 + 1486 + 1488 + 1490 + 1492 + 1494 + 1496 + 1498 + 1500 + 1502 + 1504 + 1506 + 1508 + 1510 + 1512 + 1514 + 1516 + 1518 + 1520 + 1522 + 1524 + 1526 + 1528 + 1530 + 1532 + 1534 + 1536 + 1538 + 1540 + 1542 + 1544 + 1546 + 1548 + 1550 + 1552 + 1554 + 1556 + 1558 + 1560 + 1562 + 1564 + 1566 + 1568 + 1570 + 1572 + 1574 + 1576 + 1578 + 1580 + 1582 + 1584 + 1586 + 1588 + 1590 + 1592 + 1594 + 1596 + 1598 + 1600 + =

Therefore,
is the sum of first 800 even numbers.