Question

If $$a,{a_1},{a_2},{a_3},.....,{a_{2n}},b$$     are in A.P. and $$a,{g_1},{g_2},{g_3},.....,{g_{2n}},b$$     are in G.P. and $$h$$ is the HM of $$a$$ and $$b$$ then $$\frac{{{a_1} + {a_{2n}}}}{{{g_1}{g_{2n}}}} + \frac{{{a_2} + {a_{2n - 1}}}}{{{g_2}{g_{2n - 1}}}} + ..... + \frac{{{a_n} + {a_{n + 1}}}}{{{g_n}{g_{n + 1}}}}$$         is equal to

A. $$\frac{{2n}}{h}$$  
B. $$2nh$$
C. $$nh$$
D. $$\frac{{n}}{h}$$
Answer :   $$\frac{{2n}}{h}$$
Solution :
$$\eqalign{ & {\text{Here, }}a + b = {a_1} + {a_{2n}} = {a_2} + {a_{2n - 1}} = ..... = {a_n} + {a_{n + 1}} \cr & {\text{and }}ab = {g_1}.{g_{2n}} = {g_2}.{g_{2n - 1}} = ..... = {g_n}.{g_{n + 1}}\,\,{\text{and }}h = \frac{{2ab}}{{a + b}}. \cr} $$

Releted MCQ Question on
Algebra >> Sequences and Series

Releted Question 1

If $$x, y$$ and $$z$$ are $${p^{{\text{th}}}},{q^{{\text{th}}}}\,{\text{and }}{r^{{\text{th}}}}$$   terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}{y^{z - x}}{z^{x - y}}$$   is equal to:

A. $$xyz$$
B. 0
C. 1
D. None of these
View Answer
Releted Question 2

The third term of a geometric progression is 4. The product of the first five terms is

A. $${4^3}$$
B. $${4^5}$$
C. $${4^4}$$
D. none of these
View Answer
Releted Question 3

The rational number, which equals the number $$2.\overline {357} $$   with recurring decimal is

A. $$\frac{{2355}}{{1001}}$$
B. $$\frac{{2379}}{{997}}$$
C. $$\frac{{2355}}{{999}}$$
D. none of these
View Answer
Releted Question 4

If $$a, b, c$$  are in G.P., then the equations $$a{x^2} + 2bx + c = 0$$     and $$d{x^2} + 2ex + f = 0$$     have a common root if $$\frac{d}{a},\frac{e}{b},\frac{f}{c}$$   are in-

A. A.P.
B. G.P.
C. H.P.
D. none of these
View Answer

Practice More Releted MCQ Question on
Sequences and Series

Practice More MCQ Question on Maths Section

AlgebraSequences and SeriesQuadratic EquationComplex NumberMatrices and DeterminantsPermutation and CombinationBinomial TheoremMathematical InductionMathematical Reasoning
Statistics and ProbabilityStatisticsProbability
CalculusSets and RelationsFunctionLimitsContinuityDifferentiability and DifferentiationApplication of DerivativesDifferential EquationsIndefinite IntegrationDefinite IntegrationApplication of Integration
GeometryStraight LinesCircleParabolaEllipseHyperbolaLocus3D Geometry and VectorsThree Dimensional Geometry
TrigonometryTrigonometric Ratio and IdentitiesTrignometric EquationsProperties and Solutons of TriangleInverse Trigonometry Function