Discussion

1 + 3 + 5 + ........ 33 + 35 =

Answer: A

The sum is 324.

The series adds consecutive odd numbers from 1 to 35. First count the terms, then use the fact that the sum of the first n odd numbers is n squared.

\[ \begin{aligned} n &= \frac{35 + 1}{2} = 18 \\ S &= n^{2} = 18^{2} = 324 \end{aligned} \]

The same result comes from the arithmetic series formula, number of terms times the average of the first and last terms:

\[ S = \frac{18}{2}(1 + 35) = 9 \times 36 = 324 \]

The other options are not the square of the number of terms; 423 simply reverses the digits of the correct answer.

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