Sequence and Series questions
1035 published questions with worked solutions.
- Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then the...
- If (10)^9+2(11)^1(10)^8+3(11)^2(10)^7+ +10(11)^9=k(10)^9, then k is equal to
- The sum of first 20 terms of the sequence 0.7,0.77,0.777, , is
- If a_1,a_2,a_3, are in a harmonic progression with a_1=5 and a_ 20 =25. Then, the least positive integer n for which a_n<0, is
- If the sum of the first ten terms of the series (1 35 )^2+ (2 25 )^2+ (3 15 )^2+4^2+ (4 45 )^2+ , is 16 5m, then m is equal to
- The sum of first 9 terms of the series 1^3 1+ 1^3+2^3 1+3 + 1^3+2^3+3^3 1+3+5 + is
- If the sum of the first n terms of the series 5+ 125 + 405 + 845 + is 276 5, then find the value of n.
- Let a,b and c be the 4^ th , 8^ th and 16^ th terms respectively of a non-constant A.P. If a,b,c are three consecutive terms of a...
- Find the value of 1+ 1^3+2^3 1+2 + 1^3+2^3+3^3 1+2+3 + + 1^3+2^3+3^3+ +12^3 1+2+3+ +12 - 15 (1^2+2^2+3^2+ +12^2 ).
- If the sum and product of the first three terms in an A.P. are 42 and 2394, then find the 15^ th term. [Common difference (d)>0]
- Find the least value of k for which 3^ 1+x +3^ 1-x , k2, 9^x+9^ -x are three consecutive terms of an A.P.
- If the sum of 1^ st term, 9^ th term and 23^ rd term of an A.P. is 69, then find the sum of first 21 terms.
- If 3^ 2 2 -1 , 14 and 3^ 4-2 2 are the first three terms of an A.P., then find its 7^ th term.
- Find the value of 1 17 - 16 - 1 18 - 17 + 1 19 - 18 - - 1 144 - 143 .
- If the sum of the first 12 terms of the series 1+6+ 9 (1^2+2^2+3^2 ) 7+ 12 (1^2+2^2+3^2+4^2 ) 9+ is 259m 3, then find the value...
- If the sum of the series 1+ 23+ 69+ 10 27 + 14 81 + is 2m-5 then find the value of m.
- If the A.M. of two numbers is greater than G.M. by 2 and the ratio of the numbers is 4:1, then find the sum of two numbers.
- The product of three consecutive terms of a G.P. is 216. If 3 is added to each of the first and the second of these terms, the...
- Let a be the arithmetic mean of two positive numbers and b,c be the two geometric means between them. Find the value of b^3+c^3...
- The sum of three consecutive terms in a geometric progression is 14. If 1 is added to each of the first and second terms and 1 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