Test: JEE Main 35 Year PYQs- Sequences & Series - JEE MCQ

4. Fifth term of a GP is 2, then the product of its 9 terms is [2002]

Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is [2002]

1³ – 2³ + 3³ – 4³ +...+9³  = [2002]

The sum of the series             [2003]

 up to ∞ is equal to

 is equal to

Let T_r be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers

  and  , then a – d equals [2004]

The  sum of the first n terms of the series

 is       when n is even. When n is odd the sum is                      [2004]

If the coefficients of r th, (r + 1)th, and (r + 2)th terms in the the binomial expansion of (1 + y)^m are in A.P., then m and r satisfy the equation [2005]

The sum of series         is [2004]

IF  where a, b, c are in AA..PP and |a | < 1, | b | < 1, | c | < 1 then x, y, z ar e in [2005]

The sum of the series [2005]

.................ad inf. is

Let a₁,a₂ ,a₃ ............ be terms on A.P. If then  equals [2006]

 If a₁ , a₂ , ........,a_n are in H.P., then the expression a₁a₂ + a₂ a₃ + ..........+ a_{n -1}a_n is equal to [2006]

The sum of series ... upto infinity is [2007]

In a geometric progression consisting of positive terms, each term equals the sum of the next two  terms. Then the common ratio of its progression is equals [2007]

The first two terms of a geometric progression add up to 12. the sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is [2008]

The sum to infinite term of the series       [2009]

A person is to count 4500 currency notes. Let a_n denote the number of notes he counts in the n^th minute. If a₁ = a₂ = ... = a₁₀ = 150 and a₁₀, a₁₁, ... are in an AP with common difference –2, then the time taken by him to count all notes is [2010]

A man saves 200 in each of the first three months of his service. In each of the subsequent months his saving increases by 40 more than the saving of immediately previous month. His total saving from the start of service will be 11040 after [2011]

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. [2012] 

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,....., is [JEE M 2013]

If (10)⁹ + 2(11)¹ (10⁸) + 3(11)² (10)⁷ + K........  +10 (11)⁹ = k (10)⁹, then k is equal to: [JEE M 2014]

Three positive numbers form an increasing G. P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is: [JEE M 2014]

The sum of first 9 terms of the series.     [JEE M 2015]

If m is the A.M. of two distinct real numbers l and n(l, n > 1) and G₁, G₂ and G₃ are three geometric means between l and n, then   equals : [JEE M 2015]

If the 2^nd, 5^th and 9^th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is : [JEE M 2016]

If th e sum of th e fir st ten ter ms of th e series

then m is equal to : [JEE M 2016]