A.P LECTURE 1

If a ,1/b ,c and 1/p ,q ,1/r form two arithmetic progressions of the common difference, then a ,q ,c are in A.P. if p ,b ,r are in A.P. b. 1/p ,1/b ,1/r are in A.P. c. p ,b ,r are in G.P. d. none of these

1,3,9 can be terms of (A) an A.P.but not of a G.P (B) G.P. but not of an A.P. (C) A.P. and G.P both (D) neither A.P nor G.P

If a, b, c are in A.P., then prove that : (i) b+c,c+a,a+b" are also in A.P." (ii) (1)/(bc),(1)/(ca),(1)/(ab)" are also in A.P." (iii) (a(b+c))/(bc),(b(c+a))/(ca),(c(a+b))/(ab)" are also in A.P."

If a^2,b^2,c^2 are in A.P., then prove that the following are also in A.P. Prove 1/(b+c),1/(c+a),1/(a+b)

If three positive numbers a, b, c are in A.P. and 1/a^2,1/b^2,1/c^2 also in A.P. then

If the n^(t h) term of an A.P. is (2n+1), find the sum of first n terms of the A.P.

The sum of first seven terms of an A.P is 182. If its 4^(th) term and 17^(th) term are in the ratio 1:5 then Find the A.P

The nth term of an A.P. is 4n -1 . Write down the first 4 terms and the 18 th term of the A.P..