Sequences and Series

Which term of an A.P. 7-4i, 6 - 2i, 5-0i, 4+ 2i,......... is (i) purely real(ii) purely imaginary ?

Find the 2nd and the rth term of an A.P. whose 6th and 8th terms are 12 and 22 respectively

4th term of an A.P.is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.

Find the next two terms of an A.P. given by :
(i) 2,5,8,11, ....,.......,
(ii) 1,-3,-7,-11 , .,... ,
(iii) 2x-3y,x-4y,-5y,-x-6y, ............,
(iv)1,5/6,2/3,1/2,.........,.........,

The nth term of a progression is 3n + 1, prove that it is an A.P. Find its 6th term.

How many terms are there in the A.P.
(i) 10,13,16,.......... , 49 (ii) 7,13,19,........., 199 (iii) 14 1/2,12,....... ,-38?