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11+ 22+ 33+ 44+ 55+ 66+ 77+ 88+ 99+ 110+ 121+ 132+ 143+ 154+ 165+ 176+ 187+ 198+ 209+ 220+ 231+ 242+ 253+ 264+ 275+ 286+ 297+ 308+ 319+ 330+ 341+ 352+ 363+ 374+ 385+ 396+ 407+ 418+ 429+ 440+ 451+ 462+ 473+ 484+ 495+ 506+ 517+ 528+ 539+ 550+ 561+ 572+ 583+ 594+ 605+ 616+ 627+ 638+ 649+ 660+ 671+ 682+ 693+ 704+ 715+ 726+ 737+ 748+ 759+ 770+ 781+ 792+ 803+ 814+ 825+ 836+ 847+ 858+ 869+ 880+ 891+ 902+ 913+ 924+ 935+ 946+ 957+ 968+ 979+ 990+ 1001+ 1012+ 1023+ 1034+ 1045+ 1056+ 1067+ 1078+ 1089+ +1100+ 1111+ 1122+ 1133+ 1144+ 1155+ 1166+ 1177+ 1188+ 1199+ 1210+ 1221+ 1232+ 1243+ 1254+ 1265+ 1276+ 1287+ 1298+ 1309+ 1320+ 1331

Arithmetic Sequence:

$\begin{array}{|rcll|} \hline a_n &=& a_1+(n-1)\cdot d \quad & | \quad a_1 = 11 \qquad d = 11 \qquad a_n = 1331 \\ 1331 &=& 11 + (n-1)\cdot 11 \\ 1320 &=& (n-1)\cdot 11 \\ 120 &=& n-1 \\ \mathbf{121} & \mathbf{=} & \mathbf{n} \\\\ s_n &=& \frac{(a_1+a_n)}{2} \cdot n \\ s_{121} &=& \frac{(11+1331)}{2} \cdot 121 \\ s_{121} &=& \frac{1342}{2} \cdot 121 \\ s_{121} &=& 671 \cdot 121 \\ \mathbf{s_{121}} & \mathbf{=} & \mathbf{81191} \\ \hline \end{array}$