md2 Posted June 16, 2014 Share Posted June 16, 2014 (edited) next values : I : 2 + 2 ^ 2 II : 2 + 2 ^ 3 III : 2 ^ 1 + 2 ^ 2 + 2 ^ 3 Edited June 16, 2014 by md2 Link to comment Share on other sites More sharing options...
Acme Posted June 16, 2014 Share Posted June 16, 2014 next values : I : 2 + 2 ^ 2 II : 2 + 2 ^ 3 wrong to wrong No value. Last chance? Link to comment Share on other sites More sharing options...
pzkpfw Posted June 17, 2014 Share Posted June 17, 2014 The policeman's beard is half constructed. Link to comment Share on other sites More sharing options...
imatfaal Posted June 17, 2014 Share Posted June 17, 2014 next values : I : 2 + 2 ^ 2 II : 2 + 2 ^ 3 III : 2 ^ 1 + 2 ^ 2 + 2 ^ 3 2,6,10,14,18,22,26,30,34,38 Arithmetic Progression initial term = 2 common difference = 4 Link to comment Share on other sites More sharing options...
Acme Posted June 17, 2014 Share Posted June 17, 2014 2,6,10,14,18,22,26,30,34,38 Arithmetic Progression initial term = 2 common difference = 4 an = 2(2n-1) or 4n-2 n={1,2,3...} Link to comment Share on other sites More sharing options...
imatfaal Posted June 17, 2014 Share Posted June 17, 2014 an = 2(2n-1) or 4n-2 n={1,2,3...} I prefer my phrasing. APs have an initial value a_1 and following iterations have a common difference. You want to be able to shoehorn it into this a_n = a_1 +(n-1)d. Your representation are correct - but you would have to hand do any investigation to the progression; whereas many short-cut formulae are available if the phrasing is traditional Link to comment Share on other sites More sharing options...
Acme Posted June 17, 2014 Share Posted June 17, 2014 I prefer my phrasing. APs have an initial value a_1 and following iterations have a common difference. You want to be able to shoehorn it into this a_n = a_1 +(n-1)d. Your representation are correct - but you would have to hand do any investigation to the progression; whereas many short-cut formulae are available if the phrasing is traditional It is always my pleasure to append a correct addition to one of your preferred phrasings. Here is md2's AP plotted on Ulam's spiral. From this we can tell at a glance that the AP contains no Perfect Squares. {2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218, 222, 226, 230, 234, 238, 242, 246, 250, 254, 258, 262, 266, 270, 274, 278, 282, 286, 290, 294, 298, 302, 306, 310, 314, 318, 322, 326, 330, 334, 338, 342, 346, 350, 354, 358, 362, 366, 370, 374, 378, 382, 386, 390, 394, 398, 402, 406, 410, 414, 418, 422, 426, 430, 434, 438, 442, 446, 450, 454, 458, 462, 466, 470, 474, 478, 482, 486, 490, 494, 498, 502, 506, 510, 514, 518, 522, 526, 530, 534, 538, 542, 546, 550, ...} Link to comment Share on other sites More sharing options...
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