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Find the sum of 10 consecutive numbers: {:[1041+1042],[+1043+],[1044+1045],[+1046+],[1047+1048],[+1049+],[1050]:}

11. Find the sum of 1010 consecutive numbers:\newline1041+1042+1043+1044+1045+1046+1047+1048+1049+1050 \begin{array}{l} 1041+1042 \\ +1043+ \\ 1044+1045 \\ +1046+ \\ 1047+1048 \\ +1049+ \\ 1050 \end{array}

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Full solution

Q. 11. Find the sum of 1010 consecutive numbers:\newline1041+1042+1043+1044+1045+1046+1047+1048+1049+1050 \begin{array}{l} 1041+1042 \\ +1043+ \\ 1044+1045 \\ +1046+ \\ 1047+1048 \\ +1049+ \\ 1050 \end{array}
  1. Identify Arithmetic Series Formula: We know that the sum of an arithmetic series is given by the formula S=n2×(a1+an)S = \frac{n}{2} \times (a_1 + a_n), where nn is the number of terms, a1a_1 is the first term, and ana_n is the last term.
  2. Determine Values for Formula: Here, n=10n = 10, a1=1041a_1 = 1041, and an=1050a_n = 1050 (since we're adding 1010 consecutive numbers starting with 10411041).
  3. Substitute Values into Formula: Now, plug these values into the formula: S=102×(1041+1050)S = \frac{10}{2} \times (1041 + 1050).
  4. Calculate the Sum: Calculate the sum: S=5×(2091)S = 5 \times (2091).
  5. Finalize the Calculation: Finish the calculation: S=10455S = 10455.

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