Start learning →

JEE Advanced Sequences and Series — practice questions

Explore 37 free Sequences and Series questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Sequences and Series with Quill →

Sequences and Series questions and exercises with answers

Showing questions 1–30 of 37.

The arithmetic mean and geometric mean of two positive numbers are 10 and 8 respectively. The numbers are:Read the answer and worked solution →For two distinct positive real numbers, their arithmetic mean A and geometric mean G always satisfy:Read the answer and worked solution →The value of $1^3 + 2^3 + 3^3 + \cdots + 10^3$ is:Read the answer and worked solution →The sum to infinity of the series $1 + \tfrac{1}{3} + \tfrac{1}{9} + \cdots$ is:Read the answer and worked solution →In a G.P. the 5th term is 81 and the 2nd term is 3. The common ratio is:Read the answer and worked solution →The sum of the first 20 terms of an A.P. with first term 2 and common difference 3 is:Read the answer and worked solution →For $x > 0$, the minimum value of $x + \dfrac{4}{x}$ is:Read the answer and worked solution →If the sum of two positive numbers is 6 times their geometric mean, the numbers are in the ratio:Read the answer and worked solution →The value of $n$ for which $\dfrac{a^{n+1}+b^{n+1}}{a^{n}+b^{n}}$ is the geometric mean of $a$ and $b$ is:Read the answer and worked solution →Three numbers in G.P. have product 216 and sum 19. The numbers are:Read the answer and worked solution →If the A.M. and G.M. of the roots of a quadratic equation are 8 and 5 respectively, the equation is:Read the answer and worked solution →For two positive numbers, the arithmetic mean equals the geometric mean if and only if:Read the answer and worked solution →The sum $1^2 + 2^2 + \cdots + n^2$ equals:Read the answer and worked solution →Spot the term that breaks the progressionRead the answer and worked solution →Sequences that follow specific patterns are called:Read the answer and worked solution →A sequence containing a finite number of terms is called a:Read the answer and worked solution →The number at the nth position of a sequence is called the:Read the answer and worked solution →Adding the terms of a sequence produces what is called the associated:Read the answer and worked solution →The sequence 1, 1, 2, 3, 5, 8 generated by a recurrence relation is called the:Read the answer and worked solution →In a geometric progression, the fixed multiplier between terms is called the:Read the answer and worked solution →A sequence is a geometric progression if the ratio of any term to its preceding term is:Read the answer and worked solution →For a sequence to be a geometric progression, each of its terms must be:Read the answer and worked solution →The geometric mean of two positive numbers a and b is which quantity?Read the answer and worked solution →A series is finite when the sequence behind it is:Read the answer and worked solution →The compact notation for a series uses which Greek letter?Read the answer and worked solution →The sequence of successive quotients that never ends is given as an example of an:Read the answer and worked solution →A progression built by repeatedly adding a fixed number is called an:Read the answer and worked solution →For two positive real numbers, how does the arithmetic mean compare with the geometric mean?Read the answer and worked solution →If the arithmetic mean of two positive numbers is 10, their sum must be:Read the answer and worked solution →If the geometric mean of two positive numbers is 8, their product must be:Read the answer and worked solution →

Worked practice questions

The arithmetic mean and geometric mean of two positive numbers are 10 and 8 respectively. The numbers are:

  1. 10 and 8
  2. 16 and 4
  3. 12 and 8
  4. 18 and 2
Show answer and solution

Correct answer: B. 16 and 4

a+b = 2·A.M. = 20 and ab = (G.M.)² = 64. The numbers are roots of x²−20x+64=0 ⟹ 16 and 4.

Open this question →

For two distinct positive real numbers, their arithmetic mean A and geometric mean G always satisfy:

  1. A ≥ G, with equality always
  2. A = G
  3. A < G
  4. A > G
Show answer and solution

Correct answer: D. A > G

For distinct positives, A.M. > G.M. strictly (A.M. = G.M. only when the numbers are equal).

Open this question →

The value of $1^3 + 2^3 + 3^3 + \cdots + 10^3$ is:

  1. 770
  2. 2025
  3. 3025
  4. 385
Show answer and solution

Correct answer: C. 3025

Σn³ = [n(n+1)/2]². For n=10: [10·11/2]² = 55² = 3025.

Open this question →

How to practise

  1. Choose a Sequences and Series question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Sequences and Series practice for JEE Advanced. Read explanations as you go. No signup form needed to start.

Practise Sequences and Series →

More Mathematics topics

Vector Algebra and 3D GeometryStatistics and ProbabilityContinuity, Differentiability & DerivativesIntegrals and ApplicationsMatrices and DeterminantsRelations, Functions & Inverse TrigonometryStraight Lines and Conic SectionsDeterminants