Question

the sum of n terms of an ap is n2. find its common difference ​

Answer 1

Answer:2n-1

Step-by-step explanation:

Sum of n terms = n²

Sum of n-1 terms = (n-1)²

nth term = n²-(n-1)²= 2n-1

Answer 2

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

$n²=\frac{n}{2}[2a + (n - 1)d]$

$n=\frac{1}{2}[a + An]$

$2n=(a + An)$

$An=(2n - a)$

When , n = 1

$then , A1 = 2 - a$

$a = (2 - a)$

$2a=2$

$a=1$

then ,

$An= 2n - a$

Now ,

$An= a + (n - 1)d$

$2n-1 = 1 + (n - 1)d$

$2n-2= (n - 1)d$

$2(n-1) = (n-1)d$

$2 = d$

$So ,Common \: difference(d)=2$