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Sequences and Series — BITSAT Mathematics PYQs

51 previous year questions from Sequences and Series with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

51 questionsMathematicsSolutions on every page
1

If a 0, b 0, c 0 and a, b, c are distinct, then (a+b)(b+c)(c+a) is greater than

BITSAT 2024 Solution View → 2

If _ k=1 ^n k(k+1)(k-1)=p n^4+q n^3+t n^2+s n where p, q, t and s are constants, then the value of s is equal to

BITSAT 2024 Solution View → 3

There are four numbers of which the first three are in GP and the last three are in AP, whose common difference is 6 . If the first and the last numbers are equal, then two other n

BITSAT 2024 Solution View → 4

If A=1+r^a+r^ 2 a +r^ 3 a + and B =1+ r ^ b + r ^ 2 ~b + r ^ 3 ~b + , then a b is equal to

BITSAT 2024 Solution View → 5

The sum of the infinite series 1+ 5 6 + 12 6^2 + 22 6^3 + 35 6^4 + 51 6^5 + 70 6^6 + . . is equal to:

BITSAT 2024 Solution View → 6

If ⁻¹ [ 1 1+1.2 ]+ ⁻¹ [ 1 1+2.3 ]+ + ⁻¹ [ 1 1+n(n+1) ]= ⁻¹[x] , then x is equal to

BITSAT 2024 Solution View → 7

If arithmetic mean of two distinct positive real number a and b(a b) be twice their geometric mean, then a: b=

BITSAT 2024 Solution View → 8

If y= ⁻¹ 1 x^2+x+1 + ⁻¹ 1 x^2+3 x+3 + ⁻¹ 1 x^2+5 x+7 + .to n terms, then d y d x =

BITSAT 2024 Solution View → 9

The sum to infinite term of the series 1+ 2 3 + 6 3^2 + 10 3^3 + 14 3^4 + is

BITSAT 2023 Solution View → 10

If the sum of an infinite GP a, a r, a r^2, a r^3, is 15 and the sum of the squares of its each term is 150 , then the sum of a r^2, a r^4, a r^6, is :

BITSAT 2023 Solution View → 11

Let a₁, a₂, a₄₀ be in AP and h₁, h₂, . h₁₀ be in HP. If a₁=h₁=2 and a₁₀=h₁₀=3 , then a₄ h₇ is

BITSAT 2022 Solution View → 12

Let a₁, a₂, a₃ be a harmonic progression with a₁=5 and a₂₀=25 . The least positive integer n for which a_n < 0 , is

BITSAT 2022 Solution View → 13

In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common ratio 2 . If the middle term of AP be equal to the midd

BITSAT 2022 Solution View → 14

If , , [0, ] and if , , are in AP, then - - is equal to

BITSAT 2022 Solution View → 15

If the sum of a certain number of terms of the A.P. 25,22,19, is 116 then the last term is

BITSAT 2021 Solution View → 16

The sum of all odd numbers between 1 and 1000 which are divisible by 3 is

BITSAT 2021 Solution View → 17

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

BITSAT 2021 Solution View → 18

If the harmonic mean between a and b be H , then the value of 1 H -a + 1 H -b is

BITSAT 2021 Solution View → 19

If a, b, c are positive numbers, then least value of (a+b+c) ( 1 a + 1 b + 1 c ) is

BITSAT 2020 Solution View → 20

The sum of the infinite series 2² 2 ! + 2⁴ 4 ! + 2⁶ 6 ! + is equal to

BITSAT 2020 Solution View → 21

A student read common difference of an A. P. as -2 instead of 2 and got the sum of first 5 terms as -5 . Actual sum of first five terms is

BITSAT 2020 Solution View → 22

If a>0, b>0, c>0 and a, b, c are distinct, then (a+ b) (b+c)(c+a) is greater than

BITSAT 2020 Solution View → 23

If y=3 x+6 x²+10 x³+ , , then 1 3 y- 1.4 3² 2 y²+ 1.4 .7 3² 3 y³- is equal to

BITSAT 2020 Solution View → 24

If a, c, b are in G.P., then the area of the triangle formed by the lines a x+b y+c=0 with the coordinates axes is equal to

BITSAT 2020 Solution View → 25

There are four numbers of which the first three are in G.P. and the last three are in A.P., whose common difference is 6 . If the first and the last numbers are equal then two othe

BITSAT 2020 Solution View → 26

If a , b , c are in GP and log a - log 2 b , log 2 b - log 3 c and log 3 c - log a are in AP , then a , b and c are the lengths of the sides of a triangle, which is

BITSAT 2018 Solution View → 27

If &#8721; r = 1 n t r = n n + 1 n + 2 n + 3 8 , where t r denotes the r t h term of a series, then lim n &#8594; &#8734; &#8721; r = 1 n 1 t r is

BITSAT 2018 Solution View → 28

The numbers 3 2 sin 2 &#945; - 1 , 14 and 3 4 - 2 sin 2 &#945; form first three terms of an A . P . , then its fifth term is

BITSAT 2017 Solution View → 29

If cos ( x - y ) , cos x and cos ( x + y ) are in HP , then cos x sec ( y / 2 ) is equal to

BITSAT 2017 Solution View → 30

The arithmetic mean of numbers a, b , c , d , e is M . What is the value of (a-M)+(b-M)+(c-M)+( d - M )+( e - M ) ?

BITSAT 2016 Solution View → 31

The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is

BITSAT 2016 Solution View → 32

The sum to n terms of the series 1 2 + 3 4 + 7 8 + 15 16 + is

BITSAT 2016 Solution View → 33

If a, b , and c are in A.P. and also a - 2 b, 2 b- 3 c, 3 c- a are in A.P., then

BITSAT 2016 Solution View → 34

(x+ 1 x )²+ (x²+ 1 x² )²+ (x³+ 1 x³ )² . upto n terms is

BITSAT 2016 Solution View → 35

If is the complex cube root of unity, then the value of + ^ ( 1 2 + 3 8 + 9 32 + 27 128 + ) is

BITSAT 2015 Solution View → 36

The value of 3 4 + 15 16 + 63 64 + upto n terms is

BITSAT 2015 Solution View → 37

If binomial coefficients of three consecutive terms of (1+x)² are in H P , then the maximum value of n is

BITSAT 2015 Solution View → 38

If the (2 p )^ th term of a H . P . is q and the (2 q )^ th term is p , then the 2( p + q )^ th term is-

BITSAT 2014 Solution View → 39

If 1 a , 1 ~b , 1 c are in A. P., then ( 1 a + 1 ~b - 1 c ) ( 1 b + 1 c - 1 a ) is equal to

BITSAT 2014 Solution View → 40

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

BITSAT 2014 Solution View → 41

The sum of the series 1+2.2+3.2²+4.2³+ .+100.2⁹⁹ is

BITSAT 2013 Solution View → 42

If x is positive then the sum to infinity of the series 1 1+3 x - 1-3 x (1+3 x)² + (1-3 x)² (1+3 x)³ - (1-3 x)³ (1+3 x)⁴ is

BITSAT 2012 Solution View → 43

Let a₁, a₂, a₃ . be terms on A.P. If a₁+a₂+ a_ p a₁+a₂+ .+a_ q = p² q² , p q, then a₆ a₂₁ equals

BITSAT 2012 Solution View → 44

If ( p ^ th , q ^ th ) and ( r ^ th ) terms of H.P. are ( u , v , w ) respectively, then find the value of the expression ((q-r) v w+(r-p) w u+(p-q) u v ).

BITSAT 2011 Solution View → 45

If the sum of the first (2 n ) terms of (2,5,8, ) is equal to the sum of the first (n ) terms of 57,59 , (61 ). , then ( n ) is equal to

BITSAT 2011 Solution View → 46

Find the A.M. of the first ten odd numbers.

BITSAT 2011 Solution View → 47

The coefficient of (x³² ) in the expansion of ( (x^4- 1 x^3 )¹⁵ ) is:

BITSAT 2010 Solution View → 48

A wholesale merchant wants to start the business of cereal with (₹ 24000 ). Wheat is (₹ 400 ) per quintal and rice is (₹ 600 ) per quintal. He has capacity to store 200 quintal cer

BITSAT 2010 Solution View → 49

If in the expansion of ( (2^x+ 1 4^x )^n, T₃=7 T₂ ) and sum of the binomial coefficients of second and third terms is 36 , then the value of (x ) is -

BITSAT 2009 Solution View → 50

If (A ) and (B ) are (2 2 ) matrices, then which of the following is true?

BITSAT 2009 Solution View → 51

The minimum value of the function (z=4 x+3 y ) subject to the constraints (3 x+2 y 160,5 x+2 y 200 ), (x+2 y 80, x 0, y 0 ) is

BITSAT 2009 Solution View →
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