Question

the sum of the first n terms of an ap is 5n-n^2. find the nth term of this ap

Answer 1

general form of sum of AP=n/2(2a+(n-1)d)=an+(n(n-1)/2)*d=(a-(d/2))n+(d/2)n^2
comparing coefficient of n and n^2:::>d/2=-1:::>d=(-2)
and :::>(a-d/2)=5 :::>putting value of d :::>a+1=5 :::>a=4
thus AP is a+(n-1)d =4-(n-1)2

Answer 2

given Sn=5n-n^2
s1 i.e. a1=5^1-1^2
               =5-2
               =3
S2=5^2-2^2
    =10-4
    =6
a1+a2=6
3+a2=6
a2=6-3
a2=3
d=a2-a1
  =  3-3
  =0
an=a+n-1^d
an=3+n-1^o
an=3+0
an=3