Question

The sum of first n terms of an AP is given by Sn=2n2+n.then the AP is____

Answer 1

Answer:

The sum of the first n terms of an A.P. is given by S_n=2n^2+nSn=2n2+n

At n=1 , S_1=2(1)^2+1=3S1=2(1)2+1=3

At n=2 , S_2=2(2)^2+2=10S2=2(2)2+2=10

Since a_1=S_1a1=S1

S_2=a_1+a_2S2=a1+a2

So , a_1=3a1=3

a_1+a_2=10a1+a2=10

⇒3+a_2=10\Rightarrow\ a_2=73+a2=10⇒ a2=7

Also, a_2=a_1+d\Rightarrow\ d=a_2-a_1a2=a1+d⇒ d=a2−a1

d=7-3=4d=7−3=4

nth term of A.P. is given by :-

\begin{gathered}a_n=a+(n-1)d\\\\=3+(n-1)(4)\\\\= 3+4n-4\\\\=4n-1\end{gathered}an=a+(n−1)d=3+(n−1)(4)=3+4n−4=4n−1

Hence, the nth term of A.P. is 4n-1.

please mark me as brainliest