Sequence and Series questions
1035 published questions with worked solutions.
- 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...
- Let a,b,c be in AP and |a|<1, |b|<1, |c|<1. If x=1+a+a^2+ to , y=1+b+b^2+ to and z=1+c+c^2+ , then x,y,z are in
- The HM of two numbers is 4. Their AM is A and GM is G. If 2A+G^2=27, then A is equal to
- If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots of x^2-2ax+a^2=0 respectively, then
- The difference between two numbers is 48 and the difference between their arithmetic mean and their geometric mean is 18. Then,...
- Let a,b,c be in GP and 4a,5b,4c are in AP such that a+b+c=70, then value of b is
- Let a be a positive number such that the arithmetic mean of a and 2 exceeds their geometric mean by 1. Then, the value of a is
- Three numbers whose sum is 15 are in AP. If they are added by 1,4 and 19 respectively they are in GP. The numbers are
- Let , , and be four positive real numbers such that their product is unity, then the least value of (1+ )(1+ )(1+ )(1+ ) is
- If a,b,c are distinct positive real numbers and a^2+b^2+c^2=1, then 3 (a^2b^2c^2 )^ 1/3 is
- If A_1,A_2; G_1,G_2 and H_1,H_2 be two AM's, GM's and HM's between two quantities, then the value of G_1G_2 H_1H_2 is
- If AM of two numbers is twice of their GM, then the ratio of greatest number to smallest number is
- The harmonic mean between two numbers is 14 25 and the geometric mean is 24. The greater number between them is
- If a,b,c are in AP, b-a,c-b and a are in GP, then a:b:c is
- If a,a_1,a_2, ,a_ 2n ,b are in arithmetic progression and a,g_1,g_2, ,g_ 2n ,b are in geometric progression and h is the harmonic...
- If the AM and GM between two numbers are in the ratio m:n, then the numbers are in the ratio
- If the AM of two numbers be A and GM be G, then the numbers will be
- The sum to n terms of the infinite series 1.3^2+2.5^2+3.7^2+ is
- If the sum of n terms of the series 1+ 45+ 7 5^2 + 10 5^3 + is l+ 15 16 (1- 1 5^ n-1 )- 3n-2 4 (5^ n-1 ) , then l is
- 1+ 45+ 7 5^2 + 10 5^3 + to is
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration