Consider two A.P. s: `S_1:2,7,12 ,17 , 500t e r m s` `a n dS_1:1,8,15 ,22 , 300t e r m s` Find the number of common term. Also find the last common term.

Find the sum Sigma_(r=1)^(n) r/((r+1)!) . Also, find the sum of infinite terms.

In an A.P, the first term is 5 and the sum of the first two terms is 15/2 . (i) Find the common difference

If S_n=n P+(n(n-1))/2Q ,w h e r eS_n denotes the sum of the first n terms of an A.P., then find the common difference.

Consider an A.P whose n^(th) term is 5n + 1 . Find its first two terms

Find the cardinal number of the following sets. M = {p, q, r, s, t, u}

Find the first term and common difference for each of the A.P. 5,1,-3,-7

If the sum of n terms of an A.P. is given by S_n=a+b n+c n^2, w h e r ea ,b ,c are independent of n ,t h e n a=0 common difference of A.P. must be 2b common difference of A.P. must be 2c first term of A.P. is b+c

if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r in HP. . find the ratio of first term of A.P to its common difference

Consider a G.P. with first term (1+x)^(n) , |x| lt 1 , common ratio (1+x)/(2) and number of terms (n+1) . Let 'S' be sum of all the terms of the G.P. , then sum_(r=0)^(n)"^(n+r)C_(r )((1)/(2))^(r ) equals