Sum of First 500 Even Numbers

The below workout with step by step solution using easiest method, shows how to find the sum of first 500 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, .
The first term a = 2
The common difference d = 2
Total number of terms n = 500

step 2 apply the input parameter values in the AP formula
Sum = n/2 x (a + T_n)
= 500/2 x (2 + )
= (500 x 2)/ 2
= 1000/2
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 + =

Therefore,
is the sum of first 500 even numbers.