let `{a_n},{b_n},{c_n}` be sequences such that `(1) a_n+b_n+c_n=2n+1 , (2) a_nb_n+b_nc_n+c_na_n=2n-1 , (3) a_nb_nc_n=-1 , (4) a_n < b_n < c_n` then find the value of `lim_(x->oo) (na_n)`

Write the sequence with nth terms: (i) a_n=3+4n (ii) a_n=5+2n (iii) a_n=6-n (iv) a_n=9-5n

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 (vii) a_n=n^2-n+1 (viii) a_n=2n^2-3n+1 (ix) a_n=(2n-3)/6

Find the indicated terms in each of the following sequences whose nth terms are: a_n=5_n-4; a_(12) and a_(15) a_n=(3n-2)/(4n+5); a_7 and a_8 a_n=n(n-1); a_5 and a_8 a_n=(n-1)(2-n)(3+n); a_1,a_2,a_3 a_n=(-1)^nn ; a_3,a_5, a_8

Find the next five terms of each of the following sequences given by: (1) a_1=1,a_n=a_(n-1)+2,ngeq2 (2) a_1=a_2=2,a_n=a_(n-1)-3,n >2 (3) a_1=-1,a_n=(a_(n-1))/n ,ngeq2 (4) a_1=4,a_n=4a_(n-1)+3,n >1

A sequence is given {a_n} by a_n=n^2-1, n in N show that it is not an AP.

If sum_(r=1)^n r^4= a_n then sum_(r=1)^n(2r-1)^4)= (A) a_(2n)+a_n (B) a_(2n)-a_n (C) a_(2n)-16a_n (D) a_(2n)+16b_n

If a_n=(n(n+1))/2 a_4 =…..

If a_n=n/((n+1)!) then find sum_(n=1)^50 a_n

{a_n} and {b_n} are two sequences given by a_n=(x)^(1//2^n) +(y)^(1//2^n) and b_(n)=(x)^(1//2^n)-(y)^(1//2^n) for all n in N. The value of a_1 a_2 a_3……..a_n is equal to