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

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 a, b, c are in A.P., b, c, d are in G.P. and c, d, e are in H.P., then a, c, e are in

•   A.P.
•  H.P.
•  G.P.
•  No particular order

G.P.

Q2.  In a G.P. the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third numbers, the series becomes A.P., then the greatest number is

•   8
•  24
•  32
•  None of these

8

Q3.  If a, b, c are in G.P. and x, y are the arithmetic means between a, b and b, c respectively, then a/x + c/y is equal to

•   0
•  1
•  2
•  1/2

2

Q4.  If the ratio of H.M. and G.M. between two numbers a and b is then ratio of the two numbers will be

•   2:1
•   1:2
•  1:4
•  4:1

4:1

Q5.  If p, q, r are in one geometric progression and a, b, c in another geometric progression, then cp, bq , ar are in

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

G.P.

Q6.  The sum of three decreasing numbers in A.P. is 27. If are added to them respectively, the resulting series is in G.P. The numbers are

•  6, 15, 24
•   1,2,3
•  2,4,6
•  17, 9, 1

17, 9, 1

Q7.  The common difference of an A.P. whose first term is unity and whose second, tenth and thirty fourth terms are in G.P., is

•   1/2
•  1/3
•  3
•  1

1/3

Q8.  The sum of three consecutive terms in a geometric progression is 14. If 1 is added to the first and the second terms and 1 is subtracted from the third, the resulting new terms are in arithmetic progression. Then the lowest of the original term is

•  4
•   2
•   1
•  0

2

Q9.  a,g,h are arithmetic mean, geometric mean and harmonic mean between two positive numbers x and y respectively. Then identify the correct statement among the following

•  h is the harmonic mean between a and g
•  No such relation exists between a, g and h
•  g is the geometric mean between a and h
•  a is the arithmetic mean between g and h

g is the geometric mean between a and h

Q10.  Let the positive numbers a, b, c, d be in A.P., then abc, abd, acd, bcd are

•  Not in A.P./G.P./H.P
•  In A.P.
•  In G.P.
•  In H.P.

In H.P.

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Relation between A.P., G.P. and H.P. - Advance_MCQ
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