JEE Advanced Level Test: Sequences and Series- 3 - JEE MCQ

If A, G & H are respectively te A.M., G.M. & H.M. of three positive numbers a, b, & c then the equation whose roots are a, b & c is given by

If a^x = b^y = c^z = d^t and a, b, c, d are in G.P., then x, y, z, t are in

If x_i > 0, i = 1, 2,....,50 ans x₁ + x₂ + ....+x₅₀ = 50, then the minimum value of  +  + ......+equal to

If a, a₁, a₂, a₃, ....... , a_2n, b are in A.P. and a, g₁, g₂, g₃,.....g_2n, b are in G.P. and h is the harmonic mean of a and b, then + +........ .....+ , is equal to

One side of an equilateral triangle is 24 cm. The mid-points of its sides are joined to form another triangle whose mid-points are in turn joined to form still another triangle. This process continues indefinitely. Then the sum of the perimeters of all the trianlges is

If a₁, a₂....a_n are in A.P. with common difference d > 0, then the sum of the series (sin d) [cosec a₁ cosec a₂ + cosec a₂ cosec a₃ +..... ......+ cosec an – 1 cosec a_n]

An infinite GP has first term x and sum 5, then x belongs to

If S₁, S₂, S₃ are the sums of first n natural numbers, their squares, their cubes respectively, thenis equal to

If a₁, a₂, ...., a_n are in HP, then the expression a₁a₂ + a₂a₃ + ....+ an – 1 a_n is equal to

If x² + 9y² + 25z² = xyz, then x, y and z are in

The sum of all possible products of first n natural numbers taken two by two is

If G₁ and G₂ and two geometric means and A is the arithmetic means inserted between two positive numbers then the value of  is

{a_n} and {b_n} are two sequences given bya_n =  and b_n = for all n ∈ N. The value of a₁ a₂ a₃...... a_n is equal to

If 1² + 2² + 3² + ..... + 2003² = (2003) (4007) (334) and (1) (2003) + (2) (2002) + (3) (2001) +.... ....+ (2003) (1) = (2003) (334) (x)., then x equals

Sum of first fifteen terms of series 5+10+20+… is

The common difference d of the A.P. in which T₇ = 9 and T₁T₂T₇ is least is

The H.M. between two numbers is , their A.M. is A and G.M. is G. If 2A + G² = 26, then the numbers are

If 1, 2, 3.... are first terms; 1, 3, 5..... are common differences and S₁, S₂, S₃.... are sums of n terms of given p AP's; then S₁ + S₂ + S₃ + .... + S_p is equal to

For the A.P. given by a₁, a₂,...............a_n,..........., the equations satisfied are

If sum of the infinite G.P., p,1,1/p² ,1/p³,...... is 9 /2, the value of p is

If positive numbers a, b, c are in A.P. and a², b², c² are in H.P., then

If the arithmetic mean of two positive numbers a & b (a > b) is twice their geometric mean, then a : b is