Assertion (A): The sum of 4 AM, 8 between 5 and 25 is 50,
b) 19
16.
n
Reason (R): The sum of n AM, s between a and his
(a+b).
2
a) Both A and R are correct and R is the correct explanation of A
b) Both A and R are correct but R is not the correct explanation of A
c) A is correct, R is incorrect
d) A is incorrect, R is correct
Answers
Answer:
Step-by-step explanation:
The given Assertion (A) is that the sum of 4 arithmetic means (AMs) between 5 and 25 is 50, and the Reason (R) is that the sum of n AMs between a and b is equal to n times the average of a and b, which is (a+b)/2.
The sum of n arithmetic means (AMs) between a and b is given by the formula:
Sum of n AMs = n x [(a+b)/2]
(a) For the first Assertion, if we take four AMs between 5 and 25, the first term would be 5 and the common difference would be (25 - 5)/(4 + 1) = 4. Hence, the four AMs are 5, 9, 13, and 17. Adding these up gives a sum of 44, which is not equal to 50. Therefore, Assertion (A) is incorrect.
(b) For the second Assertion, the formula for the sum of n AMs between a and b is correct. Therefore, Reason (R) is correct.
Since Assertion (A) is incorrect and Reason (R) is correct, the correct option is (c) A is correct, R is incorrect.