Let us define `a_n=(x^n+ n in N` where `a_1 = 0` , If `xy+yz+zr = p`, then `x,y,z` are roots | of `u^3 +pu-a_3 = 0` .Which can be used to calculate `a_4a_5`equ a, +a +a ..

Let sequence by defined by a_1=3,a_n=3a_(n-1)+1 for all n >1

Let a_0x^n + a_1 x^(n-1) + ... + a_(n-1) x + a_n = 0 be the nth degree equation with a_0, a_1, ... a_n integers. If p/q is arational root of this equation, then p is a divisor of an and q is a divisor of a_n . If a_0 = 1 , then every rationalroot of this equation must be an integer.

Let a_1,a_2,a_3 ......, a_n are in A.P. such that a_n = 100 , a_40-a_39=3/5 then 15^(th) term of A.P. from end is

Let lta_ngt be the sequence defined by a_1=3 and a_n =3a_(n-1)+2 for all n gt1 ..Find a_3 .

If the average of ( a_1, a_2 , a_3………………. , a_n) be bar a then the average ( xa_1 , xa_2, xa_3,……………….. xa_n) , where x ne 0 ,will be …………….

If a_1,a_2,a_3 …. are in harmonic progression with a_1=5 and a_20=25 . Then , the least positive integer n for which a_n lt 0 , is :