Test: JEE Previous Year Questions- Sequence & Series- 1 - GRE MCQ

If x₁, x₂, x₃ and y₁, y₂, y₃ are both in G.P. with the same common ratio, then the points (x₁, y₁), (x₂, y₂) and (x₃, y₃)

[AIEEE- 2003]

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation-

[AIEEE- 2004]

Let T_r be the r^th term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, m ≠ n, T_m = 1/n  and T_n = 1/m, then a - d equals-

[AIEEE- 2004]

The sum of the first n terms of the series 1² + 2. 2² + 3² + 2.4² + 5² + 2.6² +..... is  when n is even. When n is odd the sum is-

[AIEEE- 2004]

 where a, b, c are in A.P. and I a I < 1, l b I < 1, I c I < 1 then x, y, z are in -

[AIEEE- 2005]

If in a ΔABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

[AIEEE- 2005]

Let a₁, a₂, a₃, ..... be terms of an A.P. 

[AIEEE- 2006]

If a₁, a₂, ..... an are in H.P., then the expression a₁a₂ + a₂a₃ +....+ a_{n –1}an is equal to –

[AIEEE- 2006]

In a geometric progressionconsisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals-

The sum to infinity of the series 

[AIEEE 2009]

A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute. If a₁ = a₂ = .... = a₁₀ = 150 and a₁₀, a₁₁ .... are in an AP with common diferencec –2, then the time taken by him to count all notes is -

[AIEEE 2010]

Statement 1 : The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... ....+(361 + 380 + 400) is 8000.
Statement 2 : for any natural number n.

 [AIEEE- 2012]

If 100 times the 100^th term of an AP with non zero common difference equals the 50 times its 50 ^th term, then the 150^th term of this AP is:

[AIEEE 2012]

Consider an infinite geometric series with first term a and common ratio r. If the sum is 4 and the second term is 3/4, then

[JEE 2000,]

If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) (c + d) satisifes the relation :

Given that α,γ are roots of the equation, Ax²–4x+1 = 0 and β, δ the roots of the equation, Bx² – 6x + 1 = 0, find values of A and B, such that

 [REE 2000, 5]

Le α, β be the roots of x² – x + p = 0 and γ, δ the roots of x² – 4x + q = 0. If α, β, γ, δ are in G.P., then the integral values of p and q respectively, are

Suppose a, b, c are in A.P. and a², b², c² are in G.P. if a < b < c and a + b + c = 3/2, then the value of a is

[JEE 2002 ]

If the sum of the first 2n terms of the A.P. 2, 5, 8,... ..........is equal to the sum of the first n terms of the A.P. 57, 59, 61,......., then n equals

Let the positive numbers a, b, c, d be in A.P. Then abc, abd, acd, bcd are

 [JEE 2001, (Scr.)]

The first term of an infinite geometric progression is x and its sum is 5. Then  

 [JEE 2004 (Scr.)]

In the quadratic equati on ax² + bx + c = 0, If Δ = b² – 4ac and α + β, α² + β², α³+ β³, are in G.P. where α , β are the roots of ax² + bx + c = 0, then    

[JEE 2005 (Scr.)]

Let V_r d enote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r – 1). Let T_r = V _{r + 1} – V_r – 2 and Q_r = T_{r + 1} – T_r for r = 1, 2,.....
The sum V₁ + V₂ + ....... + V_n  is

Let V_r denote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r – 1). Let T_r = V _{r + 1} – V_r – 2 and Q_r = T_{r + 1} – T_r for r = 1, 2,.....
T_r is always

Le t V_r d enote the sum of first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r – 1). Let T_r = V _{r + 1} – V_r – 2 and Q_r = T_{r + 1} – T_r for r = 1, 2,.....
Which one of the following is a correct statement ?

Let A₁, G₁, H₁ denote the arithmetic, geometric and harmoni c means, respectively, of two distinct positive numbers. For n ≥ 2, Let A_{n – 1} and H_{n – 1} have arithmetic, geometric and harmonic means as A_n, G_n, H_n respectively
Which one of the following statements is correct ?

G1,G2,…,Gn are said to be n geometric means between a and b if a,G1,…Gn,b is