3, 3, 3, … is an AP.

If x , y , z are in A.P. , then the value of the determinant are in A.P. , then the value of the determinant |a+2a+3a+2x a+3a+4a+2y a+4a+5a+2z| is a. 1 b. 0 c. 2a d. a

If x, y, z are in A.P. and tan^(-1)x , tan^(-1)y and t a n^(-1)z are also in A.P., then (1) 2x""=""3y""=""6z (2) 6x""=""3y""=""2z (3) 6x""=""4y""=""3z (4) x""=""y""=""z

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

For the following Aps, write the first term and the common difference: (i) 3,1, -1,-3 ,…. (ii) -5,-1,3,7 ,…….. (iii) 1/3, 5/3, 9/3, 13/3 ,……… (iv) 0.6, 1.7 , 2.8, 3.9 ,………

Let the sum of n, 2n, 3n terms of an A.P. be S_1, S_2 and S_3 , respectively, show that S_3 =3(S_2-S_1)

Example 8 Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P.

In an AP : Give a = 7 , a_(12)= 37 , d = 3, find a and S_(12) .

The sum of …….terms of on A.P. 3, 7, 11, 15,….. Will becomes 406

S_(n) is the sum of n terms of an A.P. If S_(2n)= 3S_(n) then prove that (S_(3n))/(S_(n))= 6