Question

Write the nth term of an A.P. the sum of whose n terms is $S_{n}$.

Answer 1

Answer:

The nth term of an AP is  an = Sn–Sn–1

Step-by-step explanation:

If Sn is the sum of the first n terms of an AP, then its nth term 'an' is an = Sn – Sn–1

Hence,the nth term of an AP is  an = Sn–Sn–1

For e.g :  

Sn = 4n² + 2n  …………..(1)

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

S(n – 1) = 4(n – 1)² + 2(n – 1)

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

an = (4n² + 2n) – [4(n – 1)² + 2(n – 1)]

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Answer 2

Solution:

The sum of n terms of an AP is Sn.

So, the nth term of an AP is-

$a_{n} = s_{n} - s_{n - 1}$

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