Задача {an} — арифметическая про ... лен, если a1=312, a5= 288 (на арифметическую прогрессию)

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Решение

Вы ввели [src]
{an} - арифметическая прогрессия. найти 111-й член, если a1=312, a5= 288
Найдено в тексте задачи:
Первый член: a1 = 312
n-член an (n = 110 + 1 = 111)
Разность: d = ?
Другие члены: a1 = 312
a5 = 288
Пример: ?
Найти члены от 1 до 111
Решение [src]
    a_n - a_k
d = ---------
      n - k  
d=ak+ank+nd = \frac{- a_{k} + a_{n}}{- k + n}
a_1 = a_n + d*(-1 + n)
a1=an+d(n1)a_{1} = a_{n} + d \left(n - 1\right)
            (-1 + n)*(a_n - a_k)
a_1 = a_n - --------------------
                   n - k        
a1=an(ak+an)(n1)k+na_{1} = a_{n} - \frac{\left(- a_{k} + a_{n}\right) \left(n - 1\right)}{- k + n}
    a_5 - a_1
d = ---------
        4    
d=a1+a54d = \frac{- a_{1} + a_{5}}{4}
            a_5 - a_1  
a_1 = a_5 - ---------*3
                4      
a1=a5a1+a543a_{1} = a_{5} - \frac{- a_{1} + a_{5}}{4} \cdot 3
    288 - 312
d = ---------
        4    
d=312+2884d = \frac{-312 + 288}{4}
            288 - 312  
a_1 = 288 - ---------*4
                4      
a1=(1)312+28844+288a_{1} = \left(-1\right) \frac{-312 + 288}{4} \cdot 4 + 288
d = -6
d=6d = -6
a_1 = 312
a1=312a_{1} = 312
Первый член [src]
a_1 = 312
a1=312a_{1} = 312
Разность [src]
d = -6
d=6d = -6
Пример [src]
...
Расширенный пример:
312; 306; 300; 294; 288; 282; 276; 270; 264; 258; 252; 246; 240; 234; 228; 222; 216; 210; 204; 198; 192; 186; 180; 174; 168; 162; 156; 150; 144; 138; 132; 126; 120; 114; 108; 102; 96; 90; 84; 78; 72; 66; 60; 54; 48; 42; 36; 30; 24; 18; 12; 6; 0; -6; -12; -18; -24; -30; -36; -42; -48; -54; -60; -66; -72; -78; -84; -90; -96; -102; -108; -114; -120; -126; -132; -138; -144; -150; -156; -162; -168; -174; -180; -186; -192; -198; -204; -210; -216; -222; -228; -234; -240; -246; -252; -258; -264; -270; -276; -282; -288; -294; -300; -306; -312; -318; -324; -330; -336; -342; -348...
a1 = 312
a1=312a_{1} = 312
a2 = 306
a2=306a_{2} = 306
a3 = 300
a3=300a_{3} = 300
a4 = 294
a4=294a_{4} = 294
a5 = 288
a5=288a_{5} = 288
a6 = 282
a6=282a_{6} = 282
a7 = 276
a7=276a_{7} = 276
a8 = 270
a8=270a_{8} = 270
a9 = 264
a9=264a_{9} = 264
a10 = 258
a10=258a_{10} = 258
a11 = 252
a11=252a_{11} = 252
a12 = 246
a12=246a_{12} = 246
a13 = 240
a13=240a_{13} = 240
a14 = 234
a14=234a_{14} = 234
a15 = 228
a15=228a_{15} = 228
a16 = 222
a16=222a_{16} = 222
a17 = 216
a17=216a_{17} = 216
a18 = 210
a18=210a_{18} = 210
a19 = 204
a19=204a_{19} = 204
a20 = 198
a20=198a_{20} = 198
a21 = 192
a21=192a_{21} = 192
a22 = 186
a22=186a_{22} = 186
a23 = 180
a23=180a_{23} = 180
a24 = 174
a24=174a_{24} = 174
a25 = 168
a25=168a_{25} = 168
a26 = 162
a26=162a_{26} = 162
a27 = 156
a27=156a_{27} = 156
a28 = 150
a28=150a_{28} = 150
a29 = 144
a29=144a_{29} = 144
a30 = 138
a30=138a_{30} = 138
a31 = 132
a31=132a_{31} = 132
a32 = 126
a32=126a_{32} = 126
a33 = 120
a33=120a_{33} = 120
a34 = 114
a34=114a_{34} = 114
a35 = 108
a35=108a_{35} = 108
a36 = 102
a36=102a_{36} = 102
a37 = 96
a37=96a_{37} = 96
a38 = 90
a38=90a_{38} = 90
a39 = 84
a39=84a_{39} = 84
a40 = 78
a40=78a_{40} = 78
a41 = 72
a41=72a_{41} = 72
a42 = 66
a42=66a_{42} = 66
a43 = 60
a43=60a_{43} = 60
a44 = 54
a44=54a_{44} = 54
a45 = 48
a45=48a_{45} = 48
a46 = 42
a46=42a_{46} = 42
a47 = 36
a47=36a_{47} = 36
a48 = 30
a48=30a_{48} = 30
a49 = 24
a49=24a_{49} = 24
a50 = 18
a50=18a_{50} = 18
a51 = 12
a51=12a_{51} = 12
a52 = 6
a52=6a_{52} = 6
a53 = 0
a53=0a_{53} = 0
a54 = -6
a54=6a_{54} = -6
a55 = -12
a55=12a_{55} = -12
a56 = -18
a56=18a_{56} = -18
a57 = -24
a57=24a_{57} = -24
a58 = -30
a58=30a_{58} = -30
a59 = -36
a59=36a_{59} = -36
a60 = -42
a60=42a_{60} = -42
a61 = -48
a61=48a_{61} = -48
a62 = -54
a62=54a_{62} = -54
a63 = -60
a63=60a_{63} = -60
a64 = -66
a64=66a_{64} = -66
a65 = -72
a65=72a_{65} = -72
a66 = -78
a66=78a_{66} = -78
a67 = -84
a67=84a_{67} = -84
a68 = -90
a68=90a_{68} = -90
a69 = -96
a69=96a_{69} = -96
a70 = -102
a70=102a_{70} = -102
a71 = -108
a71=108a_{71} = -108
a72 = -114
a72=114a_{72} = -114
a73 = -120
a73=120a_{73} = -120
a74 = -126
a74=126a_{74} = -126
a75 = -132
a75=132a_{75} = -132
a76 = -138
a76=138a_{76} = -138
a77 = -144
a77=144a_{77} = -144
a78 = -150
a78=150a_{78} = -150
a79 = -156
a79=156a_{79} = -156
a80 = -162
a80=162a_{80} = -162
a81 = -168
a81=168a_{81} = -168
a82 = -174
a82=174a_{82} = -174
a83 = -180
a83=180a_{83} = -180
a84 = -186
a84=186a_{84} = -186
a85 = -192
a85=192a_{85} = -192
a86 = -198
a86=198a_{86} = -198
a87 = -204
a87=204a_{87} = -204
a88 = -210
a88=210a_{88} = -210
a89 = -216
a89=216a_{89} = -216
a90 = -222
a90=222a_{90} = -222
a91 = -228
a91=228a_{91} = -228
a92 = -234
a92=234a_{92} = -234
a93 = -240
a93=240a_{93} = -240
a94 = -246
a94=246a_{94} = -246
a95 = -252
a95=252a_{95} = -252
a96 = -258
a96=258a_{96} = -258
a97 = -264
a97=264a_{97} = -264
a98 = -270
a98=270a_{98} = -270
a99 = -276
a99=276a_{99} = -276
a100 = -282
a100=282a_{100} = -282
a101 = -288
a101=288a_{101} = -288
a102 = -294
a102=294a_{102} = -294
a103 = -300
a103=300a_{103} = -300
a104 = -306
a104=306a_{104} = -306
a105 = -312
a105=312a_{105} = -312
a106 = -318
a106=318a_{106} = -318
a107 = -324
a107=324a_{107} = -324
a108 = -330
a108=330a_{108} = -330
a109 = -336
a109=336a_{109} = -336
a110 = -342
a110=342a_{110} = -342
a111 = -348
a111=348a_{111} = -348
...
Сумма [src]
    n*(a_1 + a_n)
S = -------------
          2      
S=n(a1+an)2S = \frac{n \left(a_{1} + a_{n}\right)}{2}
       111*(312 - 348)
S111 = ---------------
              2       
S111=111(348+312)2S_{111} = \frac{111 \left(-348 + 312\right)}{2}
S111 = -1998
S111=1998S_{111} = -1998
n-член [src]
a_n = a_1 + d*(-1 + n)
an=a1+d(n1)a_{n} = a_{1} + d \left(n - 1\right)
a_111 = -348
a111=348a_{111} = -348