Задача a1=-11 S111=0 (на арифметическую прогрессию)

Вы ввели

a1=-11 s111=0

Найдено в тексте задачи:

Первый член: a1 = -11

n-член an (n = 110 + 1 = 111)

Разность: d = 2*((0)/111-(-11))/(111-1)

Другие члены: a1 = -11

Пример: ?

Найти члены от 1 до 111

Пример

...

Расширенный пример:

-11; -54/5; -53/5; -52/5; -51/5; -10; -49/5; -48/5; -47/5; -46/5; -9; -44/5; -43/5; -42/5; -41/5; -8; -39/5; -38/5; -37/5; -36/5; -7; -34/5; -33/5; -32/5; -31/5; -6; -29/5; -28/5; -27/5; -26/5; -5; -24/5; -23/5; -22/5; -21/5; -4; -19/5; -18/5; -17/5; -16/5; -3; -14/5; -13/5; -12/5; -11/5; -2; -9/5; -8/5; -7/5; -6/5; -1; -4/5; -3/5; -2/5; -1/5; 0; 1/5; 2/5; 3/5; 4/5; 1; 6/5; 7/5; 8/5; 9/5; 2; 11/5; 12/5; 13/5; 14/5; 3; 16/5; 17/5; 18/5; 19/5; 4; 21/5; 22/5; 23/5; 24/5; 5; 26/5; 27/5; 28/5; 29/5; 6; 31/5; 32/5; 33/5; 34/5; 7; 36/5; 37/5; 38/5; 39/5; 8; 41/5; 42/5; 43/5; 44/5; 9; 46/5; 47/5; 48/5; 49/5; 10; 51/5; 52/5; 53/5; 54/5; 11...

a1 = -11

$$a_{1} = -11$$

a2 = -54/5

$$a_{2} = - \frac{54}{5}$$

a3 = -53/5

$$a_{3} = - \frac{53}{5}$$

a4 = -52/5

$$a_{4} = - \frac{52}{5}$$

a5 = -51/5

$$a_{5} = - \frac{51}{5}$$

a6 = -10

$$a_{6} = -10$$

a7 = -49/5

$$a_{7} = - \frac{49}{5}$$

a8 = -48/5

$$a_{8} = - \frac{48}{5}$$

a9 = -47/5

$$a_{9} = - \frac{47}{5}$$

a10 = -46/5

$$a_{10} = - \frac{46}{5}$$

a11 = -9

$$a_{11} = -9$$

a12 = -44/5

$$a_{12} = - \frac{44}{5}$$

a13 = -43/5

$$a_{13} = - \frac{43}{5}$$

a14 = -42/5

$$a_{14} = - \frac{42}{5}$$

a15 = -41/5

$$a_{15} = - \frac{41}{5}$$

a16 = -8

$$a_{16} = -8$$

a17 = -39/5

$$a_{17} = - \frac{39}{5}$$

a18 = -38/5

$$a_{18} = - \frac{38}{5}$$

a19 = -37/5

$$a_{19} = - \frac{37}{5}$$

a20 = -36/5

$$a_{20} = - \frac{36}{5}$$

a21 = -7

$$a_{21} = -7$$

a22 = -34/5

$$a_{22} = - \frac{34}{5}$$

a23 = -33/5

$$a_{23} = - \frac{33}{5}$$

a24 = -32/5

$$a_{24} = - \frac{32}{5}$$

a25 = -31/5

$$a_{25} = - \frac{31}{5}$$

a26 = -6

$$a_{26} = -6$$

a27 = -29/5

$$a_{27} = - \frac{29}{5}$$

a28 = -28/5

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

a29 = -27/5

$$a_{29} = - \frac{27}{5}$$

a30 = -26/5

$$a_{30} = - \frac{26}{5}$$

a31 = -5

$$a_{31} = -5$$

a32 = -24/5

$$a_{32} = - \frac{24}{5}$$

a33 = -23/5

$$a_{33} = - \frac{23}{5}$$

a34 = -22/5

$$a_{34} = - \frac{22}{5}$$

a35 = -21/5

$$a_{35} = - \frac{21}{5}$$

a36 = -4

$$a_{36} = -4$$

a37 = -19/5

$$a_{37} = - \frac{19}{5}$$

a38 = -18/5

$$a_{38} = - \frac{18}{5}$$

a39 = -17/5

$$a_{39} = - \frac{17}{5}$$

a40 = -16/5

$$a_{40} = - \frac{16}{5}$$

a41 = -3

$$a_{41} = -3$$

a42 = -14/5

$$a_{42} = - \frac{14}{5}$$

a43 = -13/5

$$a_{43} = - \frac{13}{5}$$

a44 = -12/5

$$a_{44} = - \frac{12}{5}$$

a45 = -11/5

$$a_{45} = - \frac{11}{5}$$

a46 = -2

$$a_{46} = -2$$

a47 = -9/5

$$a_{47} = - \frac{9}{5}$$

a48 = -8/5

$$a_{48} = - \frac{8}{5}$$

a49 = -7/5

$$a_{49} = - \frac{7}{5}$$

a50 = -6/5

$$a_{50} = - \frac{6}{5}$$

a51 = -1

$$a_{51} = -1$$

a52 = -4/5

$$a_{52} = - \frac{4}{5}$$

a53 = -3/5

$$a_{53} = - \frac{3}{5}$$

a54 = -2/5

$$a_{54} = - \frac{2}{5}$$

a55 = -1/5

$$a_{55} = - \frac{1}{5}$$

a56 = 0

$$a_{56} = 0$$

a57 = 1/5

$$a_{57} = \frac{1}{5}$$

a58 = 2/5

$$a_{58} = \frac{2}{5}$$

a59 = 3/5

$$a_{59} = \frac{3}{5}$$

a60 = 4/5

$$a_{60} = \frac{4}{5}$$

a61 = 1

$$a_{61} = 1$$

a62 = 6/5

$$a_{62} = \frac{6}{5}$$

a63 = 7/5

$$a_{63} = \frac{7}{5}$$

a64 = 8/5

$$a_{64} = \frac{8}{5}$$

a65 = 9/5

$$a_{65} = \frac{9}{5}$$

a66 = 2

$$a_{66} = 2$$

a67 = 11/5

$$a_{67} = \frac{11}{5}$$

a68 = 12/5

$$a_{68} = \frac{12}{5}$$

a69 = 13/5

$$a_{69} = \frac{13}{5}$$

a70 = 14/5

$$a_{70} = \frac{14}{5}$$

a71 = 3

$$a_{71} = 3$$

a72 = 16/5

$$a_{72} = \frac{16}{5}$$

a73 = 17/5

$$a_{73} = \frac{17}{5}$$

a74 = 18/5

$$a_{74} = \frac{18}{5}$$

a75 = 19/5

$$a_{75} = \frac{19}{5}$$

a76 = 4

$$a_{76} = 4$$

a77 = 21/5

$$a_{77} = \frac{21}{5}$$

a78 = 22/5

$$a_{78} = \frac{22}{5}$$

a79 = 23/5

$$a_{79} = \frac{23}{5}$$

a80 = 24/5

$$a_{80} = \frac{24}{5}$$

a81 = 5

$$a_{81} = 5$$

a82 = 26/5

$$a_{82} = \frac{26}{5}$$

a83 = 27/5

$$a_{83} = \frac{27}{5}$$

a84 = 28/5

$$a_{84} = \frac{28}{5}$$

a85 = 29/5

$$a_{85} = \frac{29}{5}$$

a86 = 6

$$a_{86} = 6$$

a87 = 31/5

$$a_{87} = \frac{31}{5}$$

a88 = 32/5

$$a_{88} = \frac{32}{5}$$

a89 = 33/5

$$a_{89} = \frac{33}{5}$$

a90 = 34/5

$$a_{90} = \frac{34}{5}$$

a91 = 7

$$a_{91} = 7$$

a92 = 36/5

$$a_{92} = \frac{36}{5}$$

a93 = 37/5

$$a_{93} = \frac{37}{5}$$

a94 = 38/5

$$a_{94} = \frac{38}{5}$$

a95 = 39/5

$$a_{95} = \frac{39}{5}$$

a96 = 8

$$a_{96} = 8$$

a97 = 41/5

$$a_{97} = \frac{41}{5}$$

a98 = 42/5

$$a_{98} = \frac{42}{5}$$

a99 = 43/5

$$a_{99} = \frac{43}{5}$$

a100 = 44/5

$$a_{100} = \frac{44}{5}$$

a101 = 9

$$a_{101} = 9$$

a102 = 46/5

$$a_{102} = \frac{46}{5}$$

a103 = 47/5

$$a_{103} = \frac{47}{5}$$

a104 = 48/5

$$a_{104} = \frac{48}{5}$$

a105 = 49/5

$$a_{105} = \frac{49}{5}$$

a106 = 10

$$a_{106} = 10$$

a107 = 51/5

$$a_{107} = \frac{51}{5}$$

a108 = 52/5

$$a_{108} = \frac{52}{5}$$

a109 = 53/5

$$a_{109} = \frac{53}{5}$$

a110 = 54/5

$$a_{110} = \frac{54}{5}$$

a111 = 11

$$a_{111} = 11$$

...

Первый член

a_1 = -11

$$a_{1} = -11$$

Разность

$d = 2*(S_k / k - a_1) / (k - 1)

$d = 2*(S_111 / 111 - a_1) / (111 - 1)$

$d = 2*(S_111 / 111 - a_1) / 111$

подставляем

$d = 2*((0)/111 - (-11)) / (111 - 1)$

d = 1/5

$$d = \frac{1}{5}$$

n-член

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

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

a_111 = 11

$$a_{111} = 11$$

Сумма

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

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

       111*(-11 + 11)
S111 = --------------
             2       

$$S_{111} = \frac{111 \left(-11 + 11\right)}{2}$$

S111 = 0

$$S_{111} = 0$$