Question

The nth term of an ap whose sum of n terms is sn is

Answer 1

The nth term of the series is a_{n} = a+(n-1)da

n

=a+(n−1)d

Step-by-step explanation:

Given AP series whose sum of n terms is S_{n}S

n

. we have to write the nth term of this series.

we know that sum of n terms of AP series is

S_{n}=\frac{n}{2}[2a+(n-1)d]S

n

=

2

n

[2a+(n−1)d] where d is the common difference.

a_{n} = S_{n}-S_{n-1}a

n

=S

n

−S

n−1

= \frac{n}{2}[2a+(n-1)d]-\frac{n-1}{2}[2a +((n-1)-1)d]

2

n

[2a+(n−1)d]−

2

n−1

[2a+((n−1)−1)d]

= an+\frac{n(n-1)d}{2}-(n-1)a+\frac{(n-1)(n-2)}{2}an+

2

n(n−1)d

−(n−1)a+

2

(n−1)(n−2)

= (n-n+1)a+(n-1)d[\frac{n}{2}-\frac{(n-2)}{2}(n−n+1)a+(n−1)d[

2

n

−

2

(n−2)

= a+(n-1)da+(n−1)d

Hence, the nth term of the series is a_{n} =a+(n-1)da

n

=a+(n−1)d