Question 1032441: Determine the next two numbers in the given sequence: 43, 44, 50, 53, 65, 70, 88, 95, 119...
Found 2 solutions by jorel555, Edwin McCravy:
Answer by jorel555(1290)   (Show Source):
You can put this solution on YOUR website! Taking a look at the sequence, we can derive a pattern: 43+1=44,44+6=50,50+3=53,53+12=65,65+5=70,70+18=88,etc.. Every other number is derived from the adding the sequence of odd numbers: +1,+3,+5,+7,etc--then the number after that is a multiple of 6, so you have +6,+12,+18,etc..So, the next numbers would be 119+9,119+9+30, or 128, 158.....!!!!!!
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
The general formula is the quadratic trinomial
4n^2+3n+43 where n=0,-1,1,-2,2,-3,3,-4,4,...
for n=0, 4(0)²+3(0)+43 = 4(0)+0+43 = 0+0+43 = 43
for n=-1, 4(-1)²+3(-1)+43 = 4(-1)-3+43 = 4-3+43 = 44
for n=1, 4(1)²+3(1)+43 = 4(1)+3+43 = 4+3+43 = 50
for n=-2, 4(-2)²+3(-2)+43 = 4(-4)-6+43 = 16-6+43 = 53
for n=2, 4(2)²+3(2)+43 = 4(4)+6+43 = 16+6+43 = 65
for n=-3, 4(-3)²+3(-3)+43 = 4(-9)-9+43 = 36-9+43 = 70
for n=3, 4(3)²+3(3)+43 = 4(9)+9+43 = 36+9+43 = 88
for n=-4, 4(-4)²+3(-4)+43 = 4(-16)-12+43 = 64-12+43 = 95
for n=4, 4(4)²+3(4)+43 = 4(16)+12+43 = 64+12+43 = 119
for n=-5, 4(-5)²+3(-5)+43 = 4(-25)-15+43 = 100-15+43 = 128
for n=5, 4(5)²+3(5)+43 = 4(25)+15+43 = 100+15+43 = 158
for n=-6, 4(-6)²+3(-6)+43 = 4(-36)-18+43 = 144-18+43 = 169
for n=6, 4(6)²+3(6)+43 = 4(36)+18+43 = 144+18+43 = 205
for n=-7, 4(-7)²+3(-7)+43 = 4(-49)-21+43 = 196-21+43 = 218
for n=7, 4(7)²+3(7)+43 = 4(49)+21+43 = 196+21+43 = 260
for n=-8, 4(-8)²+3(-8)+43 = 4(-64)-24+43 = 256-24+43 = 275
for n=8, 4(8)²+3(8)+43 = 4(64)+24+43 = 256+24+43 = 323
for n=-9, 4(-9)²+3(-9)+43 = 4(-81)-27+43 = 324-27+43 = 340
for n=9, 4(9)²+3(9)+43 = 4(81)+27+43 = 324+27+43 = 394
for n=-10, 4(-10)²+3(-10)+43 = 4(-100)-30+43 = 400-30+43 = 413
for n=10, 4(10)²+3(10)+43 = 4(100)+30+43 = 400+30+43 = 473
for n=-11, 4(-11)²+3(-11)+43 = 4(-121)-33+43 = 484-33+43 = 494
for n=11, 4(11)²+3(11)+43 = 4(121)+33+43 = 484+33+43 = 560
for n=-12, 4(-12)²+3(-12)+43 = 4(-144)-36+43 = 576-36+43 = 583
for n=12, 4(12)²+3(12)+43 = 4(144)+36+43 = 576+36+43 = 655
for n=-13, 4(-13)²+3(-13)+43 = 4(-169)-39+43 = 676-39+43 = 680
for n=13, 4(13)²+3(13)+43 = 4(169)+39+43 = 676+39+43 = 758
for n=-14, 4(-14)²+3(-14)+43 = 4(-196)-42+43 = 784-42+43 = 785
for n=14, 4(14)²+3(14)+43 = 4(196)+42+43 = 784+42+43 = 869
for n=-15, 4(-15)²+3(-15)+43 = 4(-225)-45+43 = 900-45+43 = 898
for n=15, 4(15)²+3(15)+43 = 4(225)+45+43 = 900+45+43 = 988
for n=-16, 4(-16)²+3(-16)+43 = 4(-256)-48+43 = 1024-48+43 = 1019
for n=16, 4(16)²+3(16)+43 = 4(256)+48+43 = 1024+48+43 = 1115
for n=-17, 4(-17)²+3(-17)+43 = 4(-289)-51+43 = 1156-51+43 = 1148
for n=17, 4(17)²+3(17)+43 = 4(289)+51+43 = 1156+51+43 = 1250
for n=-18, 4(-18)²+3(-18)+43 = 4(-324)-54+43 = 1296-54+43 = 1285
for n=18, 4(18)²+3(18)+43 = 4(324)+54+43 = 1296+54+43 = 1393
for n=-19, 4(-19)²+3(-19)+43 = 4(-361)-57+43 = 1444-57+43 = 1430
for n=19, 4(19)²+3(19)+43 = 4(361)+57+43 = 1444+57+43 = 1544
for n=-20, 4(-20)²+3(-20)+43 = 4(-400)-60+43 = 1600-60+43 = 1583
for n=20, 4(20)²+3(20)+43 = 4(400)+60+43 = 1600+60+43 = 1703
for n=-21, 4(-21)²+3(-21)+43 = 4(-441)-63+43 = 1764-63+43 = 1744
for n=21, 4(21)²+3(21)+43 = 4(441)+63+43 = 1764+63+43 = 1870
for n=-22, 4(-22)²+3(-22)+43 = 4(-484)-66+43 = 1936-66+43 = 1913
for n=22, 4(22)²+3(22)+43 = 4(484)+66+43 = 1936+66+43 = 2045
for n=-23, 4(-23)²+3(-23)+43 = 4(-529)-69+43 = 2116-69+43 = 2090
for n=23, 4(23)²+3(23)+43 = 4(529)+69+43 = 2116+69+43 = 2228
for n=-24, 4(-24)²+3(-24)+43 = 4(-576)-72+43 = 2304-72+43 = 2275
for n=24, 4(24)²+3(24)+43 = 4(576)+72+43 = 2304+72+43 = 2419
for n=-25, 4(-25)²+3(-25)+43 = 4(-625)-75+43 = 2500-75+43 = 2468
for n=25, 4(25)²+3(25)+43 = 4(625)+75+43 = 2500+75+43 = 2618
for n=-26, 4(-26)²+3(-26)+43 = 4(-676)-78+43 = 2704-78+43 = 2669
for n=26, 4(26)²+3(26)+43 = 4(676)+78+43 = 2704+78+43 = 2825
for n=-27, 4(-27)²+3(-27)+43 = 4(-729)-81+43 = 2916-81+43 = 2878
for n=27, 4(27)²+3(27)+43 = 4(729)+81+43 = 2916+81+43 = 3040
for n=-28, 4(-28)²+3(-28)+43 = 4(-784)-84+43 = 3136-84+43 = 3095
for n=28, 4(28)²+3(28)+43 = 4(784)+84+43 = 3136+84+43 = 3263
for n=-29, 4(-29)²+3(-29)+43 = 4(-841)-87+43 = 3364-87+43 = 3320
for n=29, 4(29)²+3(29)+43 = 4(841)+87+43 = 3364+87+43 = 3494
for n=-30, 4(-30)²+3(-30)+43 = 4(-900)-90+43 = 3600-90+43 = 3553
for n=30, 4(30)²+3(30)+43 = 4(900)+90+43 = 3600+90+43 = 3733
for n=-31, 4(-31)²+3(-31)+43 = 4(-961)-93+43 = 3844-93+43 = 3794
for n=31, 4(31)²+3(31)+43 = 4(961)+93+43 = 3844+93+43 = 3980
for n=-32, 4(-32)²+3(-32)+43 = 4(-1024)-96+43 = 4096-96+43 = 4043
for n=32, 4(32)²+3(32)+43 = 4(1024)+96+43 = 4096+96+43 = 4235
for n=-33, 4(-33)²+3(-33)+43 = 4(-1089)-99+43 = 4356-99+43 = 4300
for n=33, 4(33)²+3(33)+43 = 4(1089)+99+43 = 4356+99+43 = 4498
for n=-34, 4(-34)²+3(-34)+43 = 4(-1156)-102+43 = 4624-102+43 = 4565
for n=34, 4(34)²+3(34)+43 = 4(1156)+102+43 = 4624+102+43 = 4769
for n=-35, 4(-35)²+3(-35)+43 = 4(-1225)-105+43 = 4900-105+43 = 4838
for n=35, 4(35)²+3(35)+43 = 4(1225)+105+43 = 4900+105+43 = 5048
for n=-36, 4(-36)²+3(-36)+43 = 4(-1296)-108+43 = 5184-108+43 = 5119
for n=36, 4(36)²+3(36)+43 = 4(1296)+108+43 = 5184+108+43 = 5335
for n=-37, 4(-37)²+3(-37)+43 = 4(-1369)-111+43 = 5476-111+43 = 5408
for n=37, 4(37)²+3(37)+43 = 4(1369)+111+43 = 5476+111+43 = 5630
for n=-38, 4(-38)²+3(-38)+43 = 4(-1444)-114+43 = 5776-114+43 = 5705
for n=38, 4(38)²+3(38)+43 = 4(1444)+114+43 = 5776+114+43 = 5933
for n=-39, 4(-39)²+3(-39)+43 = 4(-1521)-117+43 = 6084-117+43 = 6010
for n=39, 4(39)²+3(39)+43 = 4(1521)+117+43 = 6084+117+43 = 6244
for n=-40, 4(-40)²+3(-40)+43 = 4(-1600)-120+43 = 6400-120+43 = 6323
for n=40, 4(40)²+3(40)+43 = 4(1600)+120+43 = 6400+120+43 = 6563
for n=-41, 4(-41)²+3(-41)+43 = 4(-1681)-123+43 = 6724-123+43 = 6644
for n=41, 4(41)²+3(41)+43 = 4(1681)+123+43 = 6724+123+43 = 6890
for n=-42, 4(-42)²+3(-42)+43 = 4(-1764)-126+43 = 7056-126+43 = 6973
for n=42, 4(42)²+3(42)+43 = 4(1764)+126+43 = 7056+126+43 = 7225
for n=-43, 4(-43)²+3(-43)+43 = 4(-1849)-129+43 = 7396-129+43 = 7310
for n=43, 4(43)²+3(43)+43 = 4(1849)+129+43 = 7396+129+43 = 7568
for n=-44, 4(-44)²+3(-44)+43 = 4(-1936)-132+43 = 7744-132+43 = 7655
for n=44, 4(44)²+3(44)+43 = 4(1936)+132+43 = 7744+132+43 = 7919
for n=-45, 4(-45)²+3(-45)+43 = 4(-2025)-135+43 = 8100-135+43 = 8008
for n=45, 4(45)²+3(45)+43 = 4(2025)+135+43 = 8100+135+43 = 8278
for n=-46, 4(-46)²+3(-46)+43 = 4(-2116)-138+43 = 8464-138+43 = 8369
for n=46, 4(46)²+3(46)+43 = 4(2116)+138+43 = 8464+138+43 = 8645
for n=-47, 4(-47)²+3(-47)+43 = 4(-2209)-141+43 = 8836-141+43 = 8738
for n=47, 4(47)²+3(47)+43 = 4(2209)+141+43 = 8836+141+43 = 9020
for n=-48, 4(-48)²+3(-48)+43 = 4(-2304)-144+43 = 9216-144+43 = 9115
for n=48, 4(48)²+3(48)+43 = 4(2304)+144+43 = 9216+144+43 = 9403
for n=-49, 4(-49)²+3(-49)+43 = 4(-2401)-147+43 = 9604-147+43 = 9500
for n=49, 4(49)²+3(49)+43 = 4(2401)+147+43 = 9604+147+43 = 9794
for n=-50, 4(-50)²+3(-50)+43 = 4(-2500)-150+43 = 10000-150+43 = 9893
for n=50, 4(50)²+3(50)+43 = 4(2500)+150+43 = 10000+150+43 = 10193
for n=-51, 4(-51)²+3(-51)+43 = 4(-2601)-153+43 = 10404-153+43 = 10294
for n=51, 4(51)²+3(51)+43 = 4(2601)+153+43 = 10404+153+43 = 10600
for n=-52, 4(-52)²+3(-52)+43 = 4(-2704)-156+43 = 10816-156+43 = 10703
for n=52, 4(52)²+3(52)+43 = 4(2704)+156+43 = 10816+156+43 = 11015
for n=-53, 4(-53)²+3(-53)+43 = 4(-2809)-159+43 = 11236-159+43 = 11120
for n=53, 4(53)²+3(53)+43 = 4(2809)+159+43 = 11236+159+43 = 11438
for n=-54, 4(-54)²+3(-54)+43 = 4(-2916)-162+43 = 11664-162+43 = 11545
for n=54, 4(54)²+3(54)+43 = 4(2916)+162+43 = 11664+162+43 = 11869
for n=-55, 4(-55)²+3(-55)+43 = 4(-3025)-165+43 = 12100-165+43 = 11978
for n=55, 4(55)²+3(55)+43 = 4(3025)+165+43 = 12100+165+43 = 12308
for n=-56, 4(-56)²+3(-56)+43 = 4(-3136)-168+43 = 12544-168+43 = 12419
for n=56, 4(56)²+3(56)+43 = 4(3136)+168+43 = 12544+168+43 = 12755
for n=-57, 4(-57)²+3(-57)+43 = 4(-3249)-171+43 = 12996-171+43 = 12868
for n=57, 4(57)²+3(57)+43 = 4(3249)+171+43 = 12996+171+43 = 13210
for n=-58, 4(-58)²+3(-58)+43 = 4(-3364)-174+43 = 13456-174+43 = 13325
for n=58, 4(58)²+3(58)+43 = 4(3364)+174+43 = 13456+174+43 = 13673
for n=-59, 4(-59)²+3(-59)+43 = 4(-3481)-177+43 = 13924-177+43 = 13790
for n=59, 4(59)²+3(59)+43 = 4(3481)+177+43 = 13924+177+43 = 14144
for n=-60, 4(-60)²+3(-60)+43 = 4(-3600)-180+43 = 14400-180+43 = 14263
for n=60, 4(60)²+3(60)+43 = 4(3600)+180+43 = 14400+180+43 = 14623
for n=-61, 4(-61)²+3(-61)+43 = 4(-3721)-183+43 = 14884-183+43 = 14744
for n=61, 4(61)²+3(61)+43 = 4(3721)+183+43 = 14884+183+43 = 15110
for n=-62, 4(-62)²+3(-62)+43 = 4(-3844)-186+43 = 15376-186+43 = 15233
for n=62, 4(62)²+3(62)+43 = 4(3844)+186+43 = 15376+186+43 = 15605
for n=-63, 4(-63)²+3(-63)+43 = 4(-3969)-189+43 = 15876-189+43 = 15730
for n=63, 4(63)²+3(63)+43 = 4(3969)+189+43 = 15876+189+43 = 16108
for n=-64, 4(-64)²+3(-64)+43 = 4(-4096)-192+43 = 16384-192+43 = 16235
for n=64, 4(64)²+3(64)+43 = 4(4096)+192+43 = 16384+192+43 = 16619
for n=-65, 4(-65)²+3(-65)+43 = 4(-4225)-195+43 = 16900-195+43 = 16748
for n=65, 4(65)²+3(65)+43 = 4(4225)+195+43 = 16900+195+43 = 17138
for n=-66, 4(-66)²+3(-66)+43 = 4(-4356)-198+43 = 17424-198+43 = 17269
for n=66, 4(66)²+3(66)+43 = 4(4356)+198+43 = 17424+198+43 = 17665
for n=-67, 4(-67)²+3(-67)+43 = 4(-4489)-201+43 = 17956-201+43 = 17798
for n=67, 4(67)²+3(67)+43 = 4(4489)+201+43 = 17956+201+43 = 18200
for n=-68, 4(-68)²+3(-68)+43 = 4(-4624)-204+43 = 18496-204+43 = 18335
for n=68, 4(68)²+3(68)+43 = 4(4624)+204+43 = 18496+204+43 = 18743
for n=-69, 4(-69)²+3(-69)+43 = 4(-4761)-207+43 = 19044-207+43 = 18880
for n=69, 4(69)²+3(69)+43 = 4(4761)+207+43 = 19044+207+43 = 19294
for n=-70, 4(-70)²+3(-70)+43 = 4(-4900)-210+43 = 19600-210+43 = 19433
for n=70, 4(70)²+3(70)+43 = 4(4900)+210+43 = 19600+210+43 = 19853
for n=-71, 4(-71)²+3(-71)+43 = 4(-5041)-213+43 = 20164-213+43 = 19994
for n=71, 4(71)²+3(71)+43 = 4(5041)+213+43 = 20164+213+43 = 20420
for n=-72, 4(-72)²+3(-72)+43 = 4(-5184)-216+43 = 20736-216+43 = 20563
for n=72, 4(72)²+3(72)+43 = 4(5184)+216+43 = 20736+216+43 = 20995
for n=-73, 4(-73)²+3(-73)+43 = 4(-5329)-219+43 = 21316-219+43 = 21140
for n=73, 4(73)²+3(73)+43 = 4(5329)+219+43 = 21316+219+43 = 21578
for n=-74, 4(-74)²+3(-74)+43 = 4(-5476)-222+43 = 21904-222+43 = 21725
for n=74, 4(74)²+3(74)+43 = 4(5476)+222+43 = 21904+222+43 = 22169
for n=-75, 4(-75)²+3(-75)+43 = 4(-5625)-225+43 = 22500-225+43 = 22318
for n=75, 4(75)²+3(75)+43 = 4(5625)+225+43 = 22500+225+43 = 22768
for n=-76, 4(-76)²+3(-76)+43 = 4(-5776)-228+43 = 23104-228+43 = 22919
for n=76, 4(76)²+3(76)+43 = 4(5776)+228+43 = 23104+228+43 = 23375
for n=-77, 4(-77)²+3(-77)+43 = 4(-5929)-231+43 = 23716-231+43 = 23528
for n=77, 4(77)²+3(77)+43 = 4(5929)+231+43 = 23716+231+43 = 23990
for n=-78, 4(-78)²+3(-78)+43 = 4(-6084)-234+43 = 24336-234+43 = 24145
for n=78, 4(78)²+3(78)+43 = 4(6084)+234+43 = 24336+234+43 = 24613
for n=-79, 4(-79)²+3(-79)+43 = 4(-6241)-237+43 = 24964-237+43 = 24770
for n=79, 4(79)²+3(79)+43 = 4(6241)+237+43 = 24964+237+43 = 25244
for n=-80, 4(-80)²+3(-80)+43 = 4(-6400)-240+43 = 25600-240+43 = 25403
for n=80, 4(80)²+3(80)+43 = 4(6400)+240+43 = 25600+240+43 = 25883
for n=-81, 4(-81)²+3(-81)+43 = 4(-6561)-243+43 = 26244-243+43 = 26044
for n=81, 4(81)²+3(81)+43 = 4(6561)+243+43 = 26244+243+43 = 26530
for n=-82, 4(-82)²+3(-82)+43 = 4(-6724)-246+43 = 26896-246+43 = 26693
for n=82, 4(82)²+3(82)+43 = 4(6724)+246+43 = 26896+246+43 = 27185
for n=-83, 4(-83)²+3(-83)+43 = 4(-6889)-249+43 = 27556-249+43 = 27350
for n=83, 4(83)²+3(83)+43 = 4(6889)+249+43 = 27556+249+43 = 27848
for n=-84, 4(-84)²+3(-84)+43 = 4(-7056)-252+43 = 28224-252+43 = 28015
for n=84, 4(84)²+3(84)+43 = 4(7056)+252+43 = 28224+252+43 = 28519
for n=-85, 4(-85)²+3(-85)+43 = 4(-7225)-255+43 = 28900-255+43 = 28688
for n=85, 4(85)²+3(85)+43 = 4(7225)+255+43 = 28900+255+43 = 29198
for n=-86, 4(-86)²+3(-86)+43 = 4(-7396)-258+43 = 29584-258+43 = 29369
for n=86, 4(86)²+3(86)+43 = 4(7396)+258+43 = 29584+258+43 = 29885
for n=-87, 4(-87)²+3(-87)+43 = 4(-7569)-261+43 = 30276-261+43 = 30058
for n=87, 4(87)²+3(87)+43 = 4(7569)+261+43 = 30276+261+43 = 30580
for n=-88, 4(-88)²+3(-88)+43 = 4(-7744)-264+43 = 30976-264+43 = 30755
for n=88, 4(88)²+3(88)+43 = 4(7744)+264+43 = 30976+264+43 = 31283
for n=-89, 4(-89)²+3(-89)+43 = 4(-7921)-267+43 = 31684-267+43 = 31460
for n=89, 4(89)²+3(89)+43 = 4(7921)+267+43 = 31684+267+43 = 31994
for n=-90, 4(-90)²+3(-90)+43 = 4(-8100)-270+43 = 32400-270+43 = 32173
for n=90, 4(90)²+3(90)+43 = 4(8100)+270+43 = 32400+270+43 = 32713
for n=-91, 4(-91)²+3(-91)+43 = 4(-8281)-273+43 = 33124-273+43 = 32894
for n=91, 4(91)²+3(91)+43 = 4(8281)+273+43 = 33124+273+43 = 33440
for n=-92, 4(-92)²+3(-92)+43 = 4(-8464)-276+43 = 33856-276+43 = 33623
for n=92, 4(92)²+3(92)+43 = 4(8464)+276+43 = 33856+276+43 = 34175
for n=-93, 4(-93)²+3(-93)+43 = 4(-8649)-279+43 = 34596-279+43 = 34360
for n=93, 4(93)²+3(93)+43 = 4(8649)+279+43 = 34596+279+43 = 34918
for n=-94, 4(-94)²+3(-94)+43 = 4(-8836)-282+43 = 35344-282+43 = 35105
for n=94, 4(94)²+3(94)+43 = 4(8836)+282+43 = 35344+282+43 = 35669
for n=-95, 4(-95)²+3(-95)+43 = 4(-9025)-285+43 = 36100-285+43 = 35858
for n=95, 4(95)²+3(95)+43 = 4(9025)+285+43 = 36100+285+43 = 36428
for n=-96, 4(-96)²+3(-96)+43 = 4(-9216)-288+43 = 36864-288+43 = 36619
for n=96, 4(96)²+3(96)+43 = 4(9216)+288+43 = 36864+288+43 = 37195
for n=-97, 4(-97)²+3(-97)+43 = 4(-9409)-291+43 = 37636-291+43 = 37388
for n=97, 4(97)²+3(97)+43 = 4(9409)+291+43 = 37636+291+43 = 37970
for n=-98, 4(-98)²+3(-98)+43 = 4(-9604)-294+43 = 38416-294+43 = 38165
for n=98, 4(98)²+3(98)+43 = 4(9604)+294+43 = 38416+294+43 = 38753
for n=-99, 4(-99)²+3(-99)+43 = 4(-9801)-297+43 = 39204-297+43 = 38950
for n=99, 4(99)²+3(99)+43 = 4(9801)+297+43 = 39204+297+43 = 39544
for n=-100, 4(-100)²+3(-100)+43 = 4(-10000)-300+43 = 40000-300+43 = 39743
for n=100, 4(100)²+3(100)+43 = 4(10000)+300+43 = 40000+300+43 = 40343
Edwin
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