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» Let S_n denotes the sum of first n terms of the AP. ∴ S_n = 5n - n² \(\Rightarrow\) S_n-1 = 5(n - 1) - (n - 1)² = 5n - 5 - n² + 2n - 1 = 7n - n² - 6 ∴ n^th term of the AP, an = S_n - s_n-1 = (5n - n²) - (7n - n² - 6) Thus, the nth term of the AP is (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»

Let S_n denotes the sum of first n terms of the AP.

∴ S_n = 5n - n²

\(\Rightarrow\) S_n-1 = 5(n - 1) - (n - 1)²

= 5n - 5 - n² + 2n - 1

= 7n - n² - 6

∴ n^th term of the AP, an = S_n - s_n-1

= (5n - n²) - (7n - n² - 6)

Thus, the nth term of the AP is (6 - 2n).