Determine k so that k+2, 4k-6 and 3k-2 are three consecutive terms of an A.P.

Determine k so that : 2/3, k, 5/8 , are the three consecutive terms of an A.P.

Determine k so that : 8k + 4, 6k-2, 2k-7, are the three consecutive terms of an A.P.

If a, b and c are three consecutive terms of an A.P.,prove that k^a, k^b and k^c are three consecutive terms of a G.P. Assume k to be a non-zero real number.

If 1/(x+y),1/(2y),1/(y+z) are three consecutive terms of an A.P., prove that x, y, z are three consecutive terms of a G.P.

Prove that the product of any k consecutive integers is divisible by k! .

Find k if the points (2,-3), (k , 1) and (0,4) are collinear.

Find k so that the points (3,-2), (k,2), (8,8) are collinear.

Determine the value of k so that following functions are continuous at x = 0 f(x) = {{:((sin 2x)/(x)"," ,"if " x != 0),(k",","if " x = 0):}

Determine the value of k so that the lie joining the points A(k,1,-1), B(2,0,2k) is perpendicular to the line joining the points C(4,2k,1) and D(2,3,2)

We are given an A.P. with 1st term a and common difference d. If each of its terms is increased by the same quantity k, is the resulting progression also an A.P. ? If so, find its common difference.