Question

If the sum of first n term of an ap is given by sn=3n^+4n determine the ap and the nth term

Answer 1

Let the sum of first n terms of the A.P.=Sn  

 Given: Sn = 3n2 – 4n    ...(i)

 Now,

Replacing n by (n –1) in (i), we get,

 Sn – 1 = 3(n – 1)2 – 4(n – 1)

 nth term of the A.P. an = Sn – Sn – 1

 ∴ an = (3n2 – 4n) – [3(n – 1)2 – 4(n – 1)]

⇒ an = 3 [ n2 – (n – 1)2] – 4 [n – (n – 1)]

⇒ an = 3 (n2 – n2 + 2n – 1) – 4 (n – n + 1)

⇒ an = 3(2n –1) – 4

⇒ an = 6n – 3 – 4  

⇒ an= 6n – 7

Thus, the nth term of the A.P = 6n – 7.

so,Put n=1

a1= 6-7=-1

a2=6(2)-7=5

d=a2-a1

 =5-(-1)=6

a12=a+11d=(-1)+11(6)=65