Question

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

Answer 1

Answer:

common difference ,d =   2

Step-by-step explanation:

let the n = 1

sum of first 1 term = 1

first term of an A.P is a , = 1

let the , n= 2

sum of first 2 term , =  n² = 4

second term of an A.P. is  =  sum of first 2 term - sum of first 1 term

a2 = 4 - 1 =3

let the n = 3

sum of first 3 term , =  n² = 9

third term of an A.P. is  =  sum of first 3 term - sum of first 2 term

a3  = 9 - 4 = 5

common difference = a2 - a1 = a3 - a2

3 - 1 = 5 - 3 = 2

Answer 2

Step-by-step explanation:

Let a and d with the first term and common differential respectivily

s=n/2(2a+(n-1)d)=n^2

s=2a+(n-1)d=2n

s=(n-1)d=2n-2a

d=(2n-2a)/(n-1)

d=(2(n-a)/(n-1))