Determining `T_n` if `S_n` is given

A sequence is called an A.P if the difference of a term and the previous term is always same i.e if a_(n+1)- a_(n)= constant ( common difference ) for all n in N For an A.P whose first term is 'a ' and common difference is d has n^(th) term as t_n=a+(n-1)d Sum of n terms of an A.P. whose first term is a, last term is l and common difference is d is S_(n) = n/2 (2a +(n-1)d)=n/2 (a+a+(n-1)d)= n/2 (a+l) If sum of n terms S_n for a sequence is given by S_n=An^2+Bn+C , then sequence is an A.P. whose common difference is

Determine value of n or sum of terms if n^(th) term (T_(n)) is given

Let t_(r)=r! and S_(n)=sum_(r=1)^(n)t_(r), (n>10) then remainder when S_(n) is divided by 24 is:

The correct order of s_(n),c_(n) and T_(n) is given by

If the sum of first n terms of an A.P. is given by S=3n^(2)+4n. Determine the A.P. and the n^(th) term.