## Relation between A.P., G.P. and H.P. - Basic

Relation Between AP, GP and HP. Progression also known as sequence or series, are the types of numbers which are placed in a particular order to form a recognizable table. Simply we can say that harmonic progression is the reciprocal of the values of the terms in arithmetic progression.

Q1.  If three numbers be in G.P., then their logarithms will be in

•   A.P.
•  G.P.
•  H.P.
•  None of these

A.P.

Q2.  If the arithmetic, geometric and harmonic means between two distinct positive real numbers be A, G and H respectively, then the relation between them

•   A>G>H
•   A>G
•  A=G=H
•  None of these

A>G>H

Q3.  The geometric mean of two numbers is 6 and their arithmetic mean is 6.5. The numbers are

•   (6,12)
•  (4,9)
•  (9,12)
•   (6,7)

(4,9)

Q4.  In the four numbers first three are in G.P. and last three in A.P. whose common difference is 6. If the first and last numbers are same, then first will be

•   2
•   4
•  6
•  8

8

Q5.  If the A.M. and H.M. of two numbers is 27 and 12 respectively, then G.M. of the two numbers will be

•  9
•  18
•  6
•  12

18

Q6.  If G.M. =18 and A.M.=27, then H.M. is

•  6
•   3
•  12
•  9

12

Q7.  If sum of A.M. and H.M. between two numbers is 25 and their G.M. is 12, then sum of numbers is

•   18
•  6
•  32
•  12

32

Q8.  The numbers 1,4, 16 can be three terms (not necessarily consecutive) of

•  No A.P.
•   Only one G.P.
•   Infinite number of A.P’s.
•   Infinite numbers of G.P’s

No A.P.

Q9.  In a G.P. of alternately positive and negative terms, any terms is the A.M. of the next two terms . Then the common ratio is

•  3
•   -1
•   -2
•  -3

-2

Q10.  The A.M. of two given positive numbers is 2. If the larger number is increased by 1, the G.M. of the numbers becomes equal to the A.M. of the given numbers. Then the H.M. of the given numbers is

•   3/2
•   2/3
•   1
•   1/3

3/2

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