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BITSAT Sequences and Series PYQs with Solutions

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

51 questionsMathematics2009–2024Answers + solutions

About Sequences and Series PYQs

Sequences and Series has 51 previous year questions in the Quantrex Academy BITSAT Mathematics bank. The 51 questions in this list come from BITSAT (51), spanning 2009 to 2024. Each question opens on its own page with the options, the correct answer and the worked solution where available.

BITSAT Sequences and Series PYQs with Solutions

About Sequences and Series PYQs

Questions by year (this list)

Sequences and Series questions with solutions

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

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

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

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

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:

If ^ -1 [(1)/(1+1.2)]+ ^ -1 [(1)/(1+2.3)]+…+ ^ -1 [(1)/(1+n(n+1))]= ^ -1 [x] , then x is equal to

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

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)=

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

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 :

Let a_1, a_2, … … a_ 40 be in AP and h_1, h_2, …. h_ 10 be in HP. If a_1=h_1=2 and a_ 10 =h_ 10 =3 , then a_4 h_7 is

Let a_1, a_2, a_3 … be a harmonic progression with a_1=5 and a_ 20 =25 . The least positive integer n for which a_n < 0 , is

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

If α, β, γ ∈[0, π] and if α, β, γ are in AP, then ( α- γ)/( γ- α) is equal to

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

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

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:

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

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

The sum of the infinite series 2^ 2 2 ! + 2^ 4 4 ! + 2^ 6 6 ! +… is equal to

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

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

If y=3 x+6 x^ 2 +10 x^ 3 +… … …, ∞, then (1)/(3) y- 1.4 3^ 2 2 y^ 2 + 1.4.7 3^ 2 3 y^ 3 -… … ∞ is equal to

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

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

If a, b, c are in GP and loga - log2b, log2b - log3c and log3c - loga are in AP , then a, b and c are the lengths of the sides of a triangle, which is

If ∑ _ r = 1 ^ n t _ r = (n(n + 1)(n + 2)(n + 3))/(8), where t _ r denotes the r ^ th term of a series, then _ n → ∞ ∑ _ r = 1 ^ n 1 t _ r is

The numbers 3 ^ 2sin2α - 1 , 14 and 3 ^ 4 - 2sin2α form first three terms of an A. P. ,& then its fifth term is

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

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) ?

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

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

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

(x+(1)/(x))^ 2 +(x^ 2 + 1 x^ 2 )^ 2 +(x^ 3 + 1 x^ 3 )^ 2 … . upto n terms is

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

The value of (3)/(4)+(15)/(16)+(63)/(64)+… upto n terms is

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

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-

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

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

The sum of the series 1+2.2+3.2^ 2 +4.2^ 3 +….+100.2^ 99 is

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

Let a_ 1 , a_ 2 , a_ 3 … … … …. be terms on A.P. If a_ 1 +a_ 2 +… … … a_ p a_ 1 +a_ 2 +… … ….+a_ q = p^ 2 q^ 2 , p ≠ q, then a_ 6 a_ 21 equals

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

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

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

The coefficient of \(x^ 32 \) in the expansion of \( (x^4-(1)/(x^3) )^ 15 is:

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

If in the expansion of \( ( 2^x+ (1)/(4^x))^ n, T_3=7 T_2\) and sum of the binomial coefficients of second and third terms is 36 , then the value of \(x\) is -

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

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

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