Question 128

The sum of the first 25 terms in the progression $$2, \frac{5}{2}, 3, ........$$ is

Solution

The first 25 terms of the given series is $$\frac{4}{2}$$, $$\frac{5}{2}$$ , $$\frac{6}{2}$$ , $$\frac{7}{2}$$, ......$$\frac{28}{2}$$

$$\therefore\ $$ Sum of first 25 terms of the given series = $$\frac{\left(4+5+6+7+.....28\right)}{2}$$

$$=\frac{\frac{25}{2}\left(4+28\right)}{2}$$

$$=\frac{\frac{25}{2}\left(32\right)}{2}$$

$$=\frac{400}{2}$$

$$=200$$

Hence, the correct answer is Option B

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