Question

If sum of n terms of an AP is 5n-n^2 find AP​

Answer 1

Given

we have given sum of n terms of an AP is 5n-n²

To Find

We have to find AP

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Sₙ = 5n-n²

put n=1

S₁= 5(1)-(1)²

S₁= 5-1=4

put n = 2

S₂= 5(2)-(2)²

S₂=10-4

S₂=6

Since , S₁=a₁

So ,first term (a) is 4

First term + second term = S₂

=>a+ a₂ = 6

=>4+a₂=6

=>a₂= 6-4

=>a₂=2

Therefore, a= 4 & a₂=2

Now,we have to find the common difference

d= a₂-a

d=2-4

d= -2

AP= a,a+d,a+2d,a+3d

AP= 4,4+(-2),4+2(-2),4+3(-2)

AP=4,2,0,-2 ..