Задача найди a7,a22,a53,a111,ари ... сии (an),если a1=2,d=-2,2 (на арифметическую прогрессию)

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найди a7,a22,a53,a111,арифметической прогрессии (an),если a1=2,d=-2,2

Найдено в тексте задачи:

Первый член: a1 = 2

n-член an (n = 110 + 1 = 111)

Разность: d = -(11/5)

Другие члены: a1 = 2

Пример: ?

Найти члены от 1 до 111

Первый член

a_1 = 2

$$a_{1} = 2$$

Разность

d = -11/5

$$d = - \frac{11}{5}$$

Пример

...

Расширенный пример:

2; -1/5; -12/5; -23/5; -34/5; -9; -56/5; -67/5; -78/5; -89/5; -20; -111/5; -122/5; -133/5; -144/5; -31; -166/5; -177/5; -188/5; -199/5; -42; -221/5; -232/5; -243/5; -254/5; -53; -276/5; -287/5; -298/5; -309/5; -64; -331/5; -342/5; -353/5; -364/5; -75; -386/5; -397/5; -408/5; -419/5; -86; -441/5; -452/5; -463/5; -474/5; -97; -496/5; -507/5; -518/5; -529/5; -108; -551/5; -562/5; -573/5; -584/5; -119; -606/5; -617/5; -628/5; -639/5; -130; -661/5; -672/5; -683/5; -694/5; -141; -716/5; -727/5; -738/5; -749/5; -152; -771/5; -782/5; -793/5; -804/5; -163; -826/5; -837/5; -848/5; -859/5; -174; -881/5; -892/5; -903/5; -914/5; -185; -936/5; -947/5; -958/5; -969/5; -196; -991/5; -1002/5; -1013/5; -1024/5; -207; -1046/5; -1057/5; -1068/5; -1079/5; -218; -1101/5; -1112/5; -1123/5; -1134/5; -229; -1156/5; -1167/5; -1178/5; -1189/5; -240...

a1 = 2

$$a_{1} = 2$$

a2 = -1/5

$$a_{2} = - \frac{1}{5}$$

a3 = -12/5

$$a_{3} = - \frac{12}{5}$$

a4 = -23/5

$$a_{4} = - \frac{23}{5}$$

a5 = -34/5

$$a_{5} = - \frac{34}{5}$$

a6 = -9

$$a_{6} = -9$$

a7 = -56/5

$$a_{7} = - \frac{56}{5}$$

a8 = -67/5

$$a_{8} = - \frac{67}{5}$$

a9 = -78/5

$$a_{9} = - \frac{78}{5}$$

a10 = -89/5

$$a_{10} = - \frac{89}{5}$$

a11 = -20

$$a_{11} = -20$$

a12 = -111/5

$$a_{12} = - \frac{111}{5}$$

a13 = -122/5

$$a_{13} = - \frac{122}{5}$$

a14 = -133/5

$$a_{14} = - \frac{133}{5}$$

a15 = -144/5

$$a_{15} = - \frac{144}{5}$$

a16 = -31

$$a_{16} = -31$$

a17 = -166/5

$$a_{17} = - \frac{166}{5}$$

a18 = -177/5

$$a_{18} = - \frac{177}{5}$$

a19 = -188/5

$$a_{19} = - \frac{188}{5}$$

a20 = -199/5

$$a_{20} = - \frac{199}{5}$$

a21 = -42

$$a_{21} = -42$$

a22 = -221/5

$$a_{22} = - \frac{221}{5}$$

a23 = -232/5

$$a_{23} = - \frac{232}{5}$$

a24 = -243/5

$$a_{24} = - \frac{243}{5}$$

a25 = -254/5

$$a_{25} = - \frac{254}{5}$$

a26 = -53

$$a_{26} = -53$$

a27 = -276/5

$$a_{27} = - \frac{276}{5}$$

a28 = -287/5

$$a_{28} = - \frac{287}{5}$$

a29 = -298/5

$$a_{29} = - \frac{298}{5}$$

a30 = -309/5

$$a_{30} = - \frac{309}{5}$$

a31 = -64

$$a_{31} = -64$$

a32 = -331/5

$$a_{32} = - \frac{331}{5}$$

a33 = -342/5

$$a_{33} = - \frac{342}{5}$$

a34 = -353/5

$$a_{34} = - \frac{353}{5}$$

a35 = -364/5

$$a_{35} = - \frac{364}{5}$$

a36 = -75

$$a_{36} = -75$$

a37 = -386/5

$$a_{37} = - \frac{386}{5}$$

a38 = -397/5

$$a_{38} = - \frac{397}{5}$$

a39 = -408/5

$$a_{39} = - \frac{408}{5}$$

a40 = -419/5

$$a_{40} = - \frac{419}{5}$$

a41 = -86

$$a_{41} = -86$$

a42 = -441/5

$$a_{42} = - \frac{441}{5}$$

a43 = -452/5

$$a_{43} = - \frac{452}{5}$$

a44 = -463/5

$$a_{44} = - \frac{463}{5}$$

a45 = -474/5

$$a_{45} = - \frac{474}{5}$$

a46 = -97

$$a_{46} = -97$$

a47 = -496/5

$$a_{47} = - \frac{496}{5}$$

a48 = -507/5

$$a_{48} = - \frac{507}{5}$$

a49 = -518/5

$$a_{49} = - \frac{518}{5}$$

a50 = -529/5

$$a_{50} = - \frac{529}{5}$$

a51 = -108

$$a_{51} = -108$$

a52 = -551/5

$$a_{52} = - \frac{551}{5}$$

a53 = -562/5

$$a_{53} = - \frac{562}{5}$$

a54 = -573/5

$$a_{54} = - \frac{573}{5}$$

a55 = -584/5

$$a_{55} = - \frac{584}{5}$$

a56 = -119

$$a_{56} = -119$$

a57 = -606/5

$$a_{57} = - \frac{606}{5}$$

a58 = -617/5

$$a_{58} = - \frac{617}{5}$$

a59 = -628/5

$$a_{59} = - \frac{628}{5}$$

a60 = -639/5

$$a_{60} = - \frac{639}{5}$$

a61 = -130

$$a_{61} = -130$$

a62 = -661/5

$$a_{62} = - \frac{661}{5}$$

a63 = -672/5

$$a_{63} = - \frac{672}{5}$$

a64 = -683/5

$$a_{64} = - \frac{683}{5}$$

a65 = -694/5

$$a_{65} = - \frac{694}{5}$$

a66 = -141

$$a_{66} = -141$$

a67 = -716/5

$$a_{67} = - \frac{716}{5}$$

a68 = -727/5

$$a_{68} = - \frac{727}{5}$$

a69 = -738/5

$$a_{69} = - \frac{738}{5}$$

a70 = -749/5

$$a_{70} = - \frac{749}{5}$$

a71 = -152

$$a_{71} = -152$$

a72 = -771/5

$$a_{72} = - \frac{771}{5}$$

a73 = -782/5

$$a_{73} = - \frac{782}{5}$$

a74 = -793/5

$$a_{74} = - \frac{793}{5}$$

a75 = -804/5

$$a_{75} = - \frac{804}{5}$$

a76 = -163

$$a_{76} = -163$$

a77 = -826/5

$$a_{77} = - \frac{826}{5}$$

a78 = -837/5

$$a_{78} = - \frac{837}{5}$$

a79 = -848/5

$$a_{79} = - \frac{848}{5}$$

a80 = -859/5

$$a_{80} = - \frac{859}{5}$$

a81 = -174

$$a_{81} = -174$$

a82 = -881/5

$$a_{82} = - \frac{881}{5}$$

a83 = -892/5

$$a_{83} = - \frac{892}{5}$$

a84 = -903/5

$$a_{84} = - \frac{903}{5}$$

a85 = -914/5

$$a_{85} = - \frac{914}{5}$$

a86 = -185

$$a_{86} = -185$$

a87 = -936/5

$$a_{87} = - \frac{936}{5}$$

a88 = -947/5

$$a_{88} = - \frac{947}{5}$$

a89 = -958/5

$$a_{89} = - \frac{958}{5}$$

a90 = -969/5

$$a_{90} = - \frac{969}{5}$$

a91 = -196

$$a_{91} = -196$$

a92 = -991/5

$$a_{92} = - \frac{991}{5}$$

a93 = -1002/5

$$a_{93} = - \frac{1002}{5}$$

a94 = -1013/5

$$a_{94} = - \frac{1013}{5}$$

a95 = -1024/5

$$a_{95} = - \frac{1024}{5}$$

a96 = -207

$$a_{96} = -207$$

a97 = -1046/5

$$a_{97} = - \frac{1046}{5}$$

a98 = -1057/5

$$a_{98} = - \frac{1057}{5}$$

a99 = -1068/5

$$a_{99} = - \frac{1068}{5}$$

a100 = -1079/5

$$a_{100} = - \frac{1079}{5}$$

a101 = -218

$$a_{101} = -218$$

a102 = -1101/5

$$a_{102} = - \frac{1101}{5}$$

a103 = -1112/5

$$a_{103} = - \frac{1112}{5}$$

a104 = -1123/5

$$a_{104} = - \frac{1123}{5}$$

a105 = -1134/5

$$a_{105} = - \frac{1134}{5}$$

a106 = -229

$$a_{106} = -229$$

a107 = -1156/5

$$a_{107} = - \frac{1156}{5}$$

a108 = -1167/5

$$a_{108} = - \frac{1167}{5}$$

a109 = -1178/5

$$a_{109} = - \frac{1178}{5}$$

a110 = -1189/5

$$a_{110} = - \frac{1189}{5}$$

a111 = -240

$$a_{111} = -240$$

...

Сумма

    n*(a_1 + a_n)
S = -------------
          2      

$$S = \frac{n \left(a_{1} + a_{n}\right)}{2}$$

       111*(2 - 240)
S111 = -------------
             2      

$$S_{111} = \frac{111 \left(-240 + 2\right)}{2}$$

S111 = -13209

$$S_{111} = -13209$$

n-член

a_n = a_1 + d*(-1 + n)

$$a_{n} = a_{1} + d \left(n - 1\right)$$

a_111 = -240

$$a_{111} = -240$$