Sum of First 350 Odd Numbers

The below workout with step by step solution using easiest method, shows how to find the sum of first 350 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, .
The first term a = 1
The common difference d = 2
Total number of terms n = 350

step 2 apply the input parameter values in the AP formula
Sum = n/2 x (a + T_n)
= 350/2 x (1 + )
= (350 x 1)/ 2
= 350/2
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 + =

Therefore,
is the sum of first 350 odd numbers.