Question 31

Assertion [A]: Sum of the first hundred even natural numbers divisible by 5 is 45050.
Reason (R): Sum of the first n-terms of an Arithmetic Progression is given by $$S=(n/2)*(a+l)$$ where a=first term, l=last term.
Choose the correct answer from the options given below.

Assertion [A]:-

First 100 even natural numbers that are divisible by 5 are - {10,20,30,......,1000}

$$Sum=\dfrac{n}{2}\left[a+l\right]$$

$$Sum=\dfrac{100}{2}\left[10+1000\right]$$

$$Sum=50\times1010$$

$$Sum=50500$$

Thus, Assertion [A] is FALSE.

Sum of the first n-terms of an Arithmetic Progression is given by $$S=(n/2)*(a+l)$$ where a=first term, l=last term.

This is TRUE, as this is the actual formula for the sum of n terms. 

Thus, Reason (R) is TRUE. 

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