a_(n)=2^(n)

Write the first five terms of each of the following sequences whose n th terms are: a_(n)=3n+2( ii) a_(n)=(n-2)/(3)a_(n)=3^(n)( iv )a_(n)=(3n-2)/(5)a_(n)=(-1)^(n)*2^(n)( vi) a_(n)=(n(n-2))/(2)a_(n)=n^(2)-n+1 (vii) a_(n)=2n^(2)-3n+1a_(n)=(2n-3)/(6)

Let n in N . If (1+x)^(n)=a_(0)+a_(1)x+a_(x)x^(2)+ . . . .+a_(n) x^(n) and a_(n-3),a_(n-2),a_(n-2),a_(n-1) are in A.P. then:

What is the value of a_(3) if a_(n)=|(n)/(2)|+|(n+1)/(2)|?

The nth term of a sequence is given by a_(n)=2n^(2)+n+1. Show that it is not an A.P.

Find the indicated terms in each of the sequences whose n^(th) term is given: a_(n)= 2n^(2) -1, a_(7)

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(1)+a_(2)…..+a_(2n)=3^(n)

Write first five terms of a sequence where n^(th) term is defined by a_(n)=n^(2)+n .

Find the first four terms of the sequences whose nth terms are given by a_(n)=2n^(2)-6