{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":3,"images":5,"macros":1,"defined_names":11,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"Sheet1","index":0,"n_rows":40,"n_cols":16,"rows_kept":40}
[null,"         The Tribonacci Sequence"]
[null,"and the Ratio of Successive Terms"]
[]
[null,"   This graphing utility lets you investigate the"]
[null,"       Tribonacci Sequence {T0, T1, T2, T3, …}"]
[null,"where each term is the sum of the previous three"]
[null,"    as well as the ratio x of the successive terms"]
[]
[]
["What is the first term T0 (from 1 to 5)?"]
[null,null,{"$f":"D11","v":2},2,{"$f":"D11+10","v":12}]
[]
["What is the second term T1 (from 1 to 5)?"]
[null,null,{"$f":"D14","v":4},4,{"$f":"D14+10","v":14}]
[{"$nulls":10},"          The first",null,{"$f":"xMax","v":20}," terms of the Tribonacci Sequence "]
["What is the third term T2 (from 1 to 5)?"]
[null,null,{"$f":"D17","v":2},2,{"$f":"D17+10","v":12},{"$nulls":5},"Which term (2 - 20) do you want displayed?"]
[{"$nulls":12},{"$f":"N18","v":19},19,{"$f":"N18+10","v":29}]
[{"$nulls":10},"             That term =",null,null,{"$f":"LOOKUP(N,Sheet2!A3:A27,Sheet2!B3:B25)","v":68370},{"$f":"\"                     = \" & TEXT(Sheet2!M14,\"#######\") &\" + \" & TEXT(Sheet2!J21,\"#######\")&\" + \" & TEXT(Sheet2!J18,\"#######\")","v":"                     = 10988 + 20210 + 37172"}]
["How many terms do you want to see (10 - 200)?"]
[null,null,{"$f":"D21*10","v":20},2,{"$f":"D21+10","v":12}]
[]
[]
["Click each item below for suggestions and investigations"]
[null,"   Item 1"]
[null,"   Item 2"]
[null,"   Item 3"]
[null,"   Item 4"]
[]
[]
["To access/download all the DIGMath Apps for College Algebra/Precalculus"]
["    Click this link:",null,"DIGMath Modules for College Algebra and Precalculus"]
[]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]
[]
[{"$nulls":9},"The ratios of the first",null,null,{"$f":"xMax","v":20},"terms approach x =",null,{"$f":"LastSum","v":1.8392868503085438}]

{"sheet":"Sheet2","index":1,"n_rows":202,"n_cols":13,"rows_kept":202}
["k","Lk","ratio","plot k's","plot T's","plot ratios","Errors"]
[]
[1,{"$f":"a0","v":2},{"$f":"B4/B3","v":2},{"$f":"A3","v":1},{"$f":"B3","v":2},{"$f":"C3","v":2},{"$f":"F3-phi","v":0.3819660112501051}]
[{"$f":"A3+1","v":2},{"$f":"b0","v":4},{"$f":"B5/B4","v":0.5},{"$f":"D3+1","v":2},{"$f":"B4","v":4},{"$f":"C4","v":0.5},-1.118033988749895,null,"a last = ",{"$f":"LOOKUP(xMax,A3:A200,C3:C200)","v":1.8392868503085438}]
[{"$f":"A4+1","v":3},{"$f":"c0","v":2},4,{"$f":"D4+1","v":3},2,4,2.381966011250105]
[4,{"$f":"B3+B4+B5","v":8},1.75,4,8,1.75,0.1319660112501051,null,"Fmax =",{"$f":"LOOKUP(xMax,A3:A203,B3:B203)","v":125752},null,"xmax=",{"$f":"xMax","v":20}]
[5,{"$f":"B4+B5+B6","v":14},1.7142857142857142,5,14,1.7142857142857142,0.09625172553581929,null,"last sum=",{"$f":"LOOKUP(xMax,A3:A203,C3:C203)","v":1.8392868503085438},null,"N =",{"$f":"N","v":19}]
[6,24,1.9166666666666667,6,{"$f":"IF(A8<=xMax,B8,FMax)","v":24},1.9166666666666667,0.29863267791677184,{"$nulls":4},"phi =",{"$f":"(1+SQRT(5))/2","v":1.618033988749895}]
[7,46,1.826086956521739,{"$f":"IF(A9<=xMax,A9,xMax)","v":7},46,1.826086956521739,0.20805296777184412,null,{"$f":"N","v":19},0]
[8,84,1.8333333333333333,8,84,{"$f":"IF(A10<=xMax,C10,lastA)","v":1.8333333333333333},0.21529934458343836,null,{"$f":"I9","v":19},{"$f":"M14","v":10988},{"$f":"J10-J9","v":10988}]
[9,154,1.844155844155844,9,154,1.844155844155844,0.2261218554059492,null,{"$f":"N","v":19},{"$f":"LOOKUP(N-2,A3:A23,B3:B23)+J10","v":31198},{"$f":"J11-J10","v":20210},"Nth term",{"$f":"LOOKUP(N,A3:A22,B3:B22)","v":68370}]
[10,284,1.8380281690140845,10,284,1.8380281690140845,0.2199941802641896,null,{"$f":"I11","v":19},{"$f":"LOOKUP(N-1,A3:A23,B3:B23)+J11","v":68370},37172,"N-1 term",{"$f":"LOOKUP(N-1,A3:A22,B3:B22)","v":37172}]
[11,522,1.839080459770115,11,522,1.839080459770115,0.22104647102022001,null,{"$f":"I12","v":19},{"$f":"LOOKUP(N,A3:A23,B3:B23)","v":68370},0,"N-2 term",{"$f":"LOOKUP(N-2,A3:A22,B3:B22)","v":20210}]
[12,960,1.8395833333333333,12,960,{"$f":"IF(A14<=xMax,C14,lastA)","v":1.8395833333333333},0.22154934458343845,{"$nulls":4},"N-3 term",{"$f":"LOOKUP(N-3,A3:A22,B3:B22)","v":10988}]
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[14,3248,1.8392857142857142,14,3248,1.8392857142857142,0.2212517255358193]
[15,5974,1.8393036491463006,15,5974,1.8393036491463006,0.22126966039640572,null,{"$f":"N-1","v":18},0]
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