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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…

Question and options

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)S = (n/2) *(a + l) where a=first term, l=last term.
Choose the correct answer from the given options.
  1. Both [A] and (R) are true and (R) is the correct explanation of (A).
  2. Both [A] and (R) are true but (R) is NOT the correct explanation of (A).
  3. [A] is true but (R) is false.
  4. [A] is false but (R) is true.

Answer and explanation

Correct answer: D - [A] is false but (R) is true.
Even numbers divisible by 5 are multiples of 10: 10, 20, ..., 1000. Their sum = (100/2)(10+1000) = 50500, not 45050, so A is false. R is the correct AP sum formula, so R is true.

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