Mathematics
Assertion (A): The sum of first n terms of the A.P. −1, 5, 11, … is 3n2 − 4n.
Reason (R): The sum of first n terms of an A.P. is given by Sn = [2a + (n − 1)d].
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
AP
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Answer
A.P. : -1, 5, 11, ……
Given,
a = -1
d = 5 - (-1) = 6
We know that,
Sn = [2a + (n − 1)d]
⇒ Sn = [2(-1) + (n − 1)6]
= [-2 + (6n − 6)]
= (6n − 8)
= 2(3n − 4)
= n(3n - 4)
= 3n2 - 4n.
∴ Assertion (A) is true.
The standard and correct formula for the sum of the first n terms of an A.P.
Sn = [2a + (n − 1)d]
∴ Reason (R) is true.
Both A and R are true, and R is the correct explanation of A.
Hence, option 1 is the correct option.
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