The sum of first n terms of an AP is (5n - n²). The nth term of the A

1.	The sum of first n terms of an AP is (5n - n²). The nth term of the AP is(a) (5-2n)(b) (6-2n)(c) (2n-5)(d) (2n-6)
Answer» Given that sum of the first n terms of an AP is 5n - n² Sn = 5n − n² First term, a₁= S₁= 5(1) − (1)2= 5 − 1 = 4 Sum of first two terms = S₂= 5(2) − (2)2= 10 − 4 = 6. Second term, a₂= S₂− S₁= 6 − 4 = 2 d = a₂− a₁= 2 − 4 = −2 an= a + (n − 1)d = 4 + (n − 1) (−2) = 4 − 2n + 2 = 6 − 2n ∴ nthterm of an A.P = 6 - 2n

The sum of first n terms of an AP is (5n - n²). The nth term of the AP is(a) (5-2n)(b) (6-2n)(c) (2n-5)(d) (2n-6)

Answer»

Given that sum of the first n terms of an AP is 5n - n²

Sn = 5n − n²

First term, a₁= S₁= 5(1) − (1)2= 5 − 1 = 4

Sum of first two terms = S₂= 5(2) − (2)2= 10 − 4 = 6.

Second term, a₂= S₂− S₁= 6 − 4 = 2

d = a₂− a₁= 2 − 4 = −2

an= a + (n − 1)d

= 4 + (n − 1) (−2)

= 4 − 2n + 2

= 6 − 2n

∴ nthterm of an A.P = 6 - 2n