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1. Find the average of first 97 natural numbers.

A. 47

B. 37

C. 48

D. 49

Solution:

1^st Method:
Average of 1^st n natural number is given by

= \frac{\frac{n \times (n + 1)}{2}}{n}

Average of 1^st 97 natural number is given by

\begin{aligned} \frac{\frac{97 \times (97 + 1)}{2}}{97} \\ = 49 \end{aligned}

2^st Method:
These numbers are in AP series so average.

\begin{aligned} = \frac{sum of corresponding term}{2} \\ = \frac{1 + 97}{2} = 49 \\ or, \frac{2 + 96}{2} = 49 \\ or, \frac{3 + 95}{2} = 49 \\ And so on . \end{aligned}

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