Mathematics
Assertion (A): If the sum of first n terms of an A.P. is given Sn = 2n2 − n, then its nth term is 4n - 3.
Reason (R): The nth term (tn) of an A.P. from the end is l - (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
We know that,
Tn = Sn - Sn - 1
Given,
Sn = 2n2 - n
Sn - 1 = 2(n - 1)2 - (n - 1)
= 2(n2 - 2n + 1) - n + 1
= 2n2 - 4n + 2 - n + 1
= 2n2 - 5n + 3.
Tn = 2n2 - n - (2n2 - 5n + 3)
= 2n2 - n - 2n2 + 5n - 3
= 4n - 3.
Assertion (A) is true.
The nth term (tn) of an A.P. from the end is l - (n - 1)d.
Reason (R) is true.
Both A and R are true, but R is not the correct explanation of A.
Hence, option 2 is the correct option.
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