Progression (Sequence and Series) Questions

The value of cot cot-1 is

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2·22 + 32 + 2·42 + 52 + 2·62 + ....... If B - 2A = 100λ, then λ is equal...

Let Then Sn can take value(s)

The sum of first 20 terms of the sequence 0.7,0.77, 0.777, ......, is :

If x, y, z are in A.P. and tan-1x, tan-1y and tan-1z are also in A.P., then

The term independent of x in expansion of 10 is :...

If 100 times the 100th term of an A.P. with non-zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is :...

Let a1, a2, a3,..... be in harmonic progression with a1 = 5 and a20 = 25. The least positive integer n forwhich an...

Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolledsimultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is...

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression sin 2C +...

The third term of a geometric progression is $4$. The product of the first five terms is:

If a, b, c are in GP, then the equations ax2 + 2bx + c = 0 and dx2 + 2bx + f = 0 have a common root, if, are in...

If a, b, c and p are distinct real numbers such that (a2 + b2 + c2) p2 - 2(ab + bc + cd) p +(b2 + c2 + d2) ≤ 0, then a, b, c, d...

In a triangle the lengths of the two larger sides are 10 and 9, respectively. If the angles are in AP, then the length of the third side can be

Sum of the first n terms of the series + ..... is equal to

The product of n positive numbers is unity, then their sum is

Let Tr be the r th term of an AP, for r = 1, 2, 3....... if for some positive integers m, n we have Tm = and Tm = , then Tm equals...

If x > 1, y > 1, z > 1 are in GP, thenare in

If x1, x2, x3 as well as y1, y2, y3 are in GP with the same common ratio, then the points (x1, y1), (x2, y2) and (x3, y3)...

The harmonic mean of the roots of the equation (5 + √2) x2 - (4 + √5)x + 8 + 2√5 = 0 is