Show thast the sequence `(t_n)` defined by `t_n = x+(2n-1)b, where x and b` are constants, is an A.P. Fid its common difference.

Show that the sequence defined by a_(n) = m + (2n - 1) d, where m and d are constants , is an A.P. Find its common difference .

Show that the sequence t_(n) defined by t_(n)=2*3^(n)+1 is not a GP.

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 is S_(n) = n/2 (2a +(n-1)d)=n/2 (a+a+(n-1)d)= n/2 (a+l) A sequence whose n^(th) term is given by t_(n) = An + N , where A,B are constants , is an A.P with common difference

Show that the sequence t_(n) defined by t_(n)=(2^(2n-1))/(3) for all values of n in N is a GP. Also, find its common ratio.

Show that the the sequence defined by T_(n) = 3n^(2) +2 is not an AP.

Show that the sequence defined by a_(n)=2n^(2)+1 is not an A.P.

If the sum of n terms of an A.P. is (pn+qn^(2)), where p and q are constants, find the common difference.

Show that the sequence defined by a_(n)=3n^(2)-5 is not an A.P.

Is the sequence defined by a_(n) = 3n^(2) + 2 an A.P. ?

If the sum of n terms of an A.P.is nP+(1)/(2)n(n-1)Q, where P and Q are constants,find the common difference.