Question

The sum of first n terms of an A.P. is 5n − $n^{2}$ . Find the nth term of this A.P.

Answer 1

Answer:

The nth term of the A.P is  - 2n + 6.

Step-by-step explanation:

Given :  

Sn = 5n - n² …………..(1)

Now , on Replacing n by (n –1) in eq (i),  

S(n – 1) = 5(n – 1) - (n – 1)²

nth term of the A.P., an = Sn – S(n – 1)

an = 5n - n² – [5(n – 1) -  (n – 1)²]

⇒ an = 5n - n² – [5(n  - 1) -   (n² + 1 - 2n)]

[(a + b)² = a² + b² - 2ab]

⇒ an = 5n - n² – [5n - 5 - n² - 1 + 2n]

⇒ an = 5n - n² – 5n + 5 + n² + 1 - 2n

⇒ an = 5n - 5n - 2n -  n² + n² + 5 + 1  

⇒ an =  - 2n + 6

Hence, the nth term of the A.P is  - 2n + 6.

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