Question

In an A.P tn=9+7n then Sn=​

Answer 1

Given: T  

n

​

=6n+5 (1)

T  

n

​

=a+(n−1)d, where a= First term, d= Difference between terms ... (2)

Equating (1) and (2)

6n+5=a+(n−1)d

6n+5= a+ nd−d  (3)

Equating n terms:6n=nd

d=6 . (4)

Substituting (4) in (3)

6n+5=a+6n−6

5=a−6

a=11 .(5)

Now

S  

n

​

=  

2

n

​

(2a+(n−1)d)

S  

n

​

=  

2

n

​

(a+T)

n

​

) (6)

Substituting (1) and (5) in (6)

S  

n

​

=  

2

n

​

(11+6n+5)  

S  

n

​

=  

2

n

​

(16+6n)  

S  

n

​

=n(8+3n)  

S  

n

​

=3n  

2

+8n