Explanation:

Let's analyze the given number series: $121, 164, 250, 379, 551, ?$\nWe will find the differences between consecutive terms:\nFirst difference ($D_1$): $164 - 121 = 43$\nSecond difference ($D_2$): $250 - 164 = 86$\nThird difference ($D_3$): $379 - 250 = 129$\nFourth difference ($D_4$): $551 - 379 = 172$ \nThe sequence of first differences is: $43, 86, 129, 172$.\nLet's examine the pattern in this sequence of differences. We can see that each term is a multiple of $43$: $43 \times 1 = 43$ $43 \times 2 = 86$ $43 \times 3 = 129$ $43 \times 4 = 172$\nThis indicates that the first differences form an arithmetic progression with a common difference of $43$. \nTo find the next term in the original series, we need to find the fifth difference ($D_5$): $D_5 = D_4 + 43 = 172 + 43 = 215$. \nNow, add this fifth difference to the last term of the original series:\nNext term $= 551 + D_5 = 551 + 215 = 766$. \nLet's evaluate the options:\nOption (1) $746$: If the next term were $746$, the difference would be $746 - 551 = 195$, which is not $215$.\nOption (2) $766$: This matches our calculated value.\nOption (3) $872$: If the next term were $872$, the difference would be $872 - 551 = 321$, which is not $215$.\nOption (4) $892$: If the next term were $892$, the difference would be $892 - 551 = 341$, which is not $215$. \nTherefore, the next term in the series is $766$. The correct option is (2) 766.