Question

If the sum of the first n terms an A.P. be n²+2n , the term of the series which has the value 201, is​

Answer 1

Answer:

The answer is 100

Step-by-step explanation:

Given sum of first n terms of an A.P. is $n^2+2n$

                     $\Rightarrow \text{S}_n=n^2+2n$

Let $a_n$ be its nth term, then

           $a_n=\text{S}_n-\text{S}_{n-1}=(n^2+2n)-((n-1)^2+2(n-1))$

                                    $=(n^2+2n)-(n^2-2n+1+2n-2)\\=n^2+2n-(n^2-1)\\=2n+1$

Also given  $a_n=201$

               $\Rightarrow 2n+1=201\\\Rightarrow 2n=201-1=200\\\Rightarrow n=\frac{200}{2}=100$