Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
2, 6, 20, 42, 110, 156, 272, .....
Assertion A: In the above number series the number is subtracted from the square of the same prime number.
Reason R: The difference between the two consecutive numbers of the series are multiple of even numbers only.
In the light of the above statements, choose the most appropriate answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A is correct but R is false
2, 6, 20, 42, 110, 156, 272, .....:
Assertion A: In the above number series the number is subtracted from the square of the same prime number.
Lets verify the assertion A:
1. 22 - 2 = 2
2. 32 - 3 = 6
3. 52 - 5 = 20
4. 72 - 7 = 42
5. 112 - 11 = 110
6. 132 - 13 = 156
7. 172 - 17 = 272
Here we can see, the assertion A is correct.
Now,
Reason R: The difference between the two consecutive numbers of the series are multiple of even numbers only.
Lets verify the Reason R:
1. 6 - 2 = 4 = 2 × 2 (True)
2. 20 - 6 = 14 = 7 × 2 (False, as 7 is not even number).
Therefore, Option (3) : A is correct but R is false is the correct answer.