## Properties of G.P. - Basic

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.

Q1.  If a, b, c are in G.P., then

•  b(c2+a2)=c(a2-b2)
•  a(b2+c2)=c(a2+b2)
•  a2(b-c)=c2(a-b)
•   None of these

a(b2+c2)=c(a2+b2)

Q2.  If x is added to each of numbers 3, 9, 21 so that the resulting numbers may be in G.P., then the value of x will be

•  3
•  1/2
•  2
•  1/3

3

Q3.  If p, q, r are in A.P., then pth, qth and rth terms of any G.P. are in

•   A.P.
•  G.P.
•  Reciprocals of these terms are in A.P.
•   None of these

G.P.

Q4.  If a, b, c are in G.P., then

•   a2,b2,c2 are in G.P.
•   a2(b+c),a2(a+b),b2(a+c) are in G.P.
•  a/b+c , b/a+c , c/a+b are in G.P.
•  None of these

a2,b2,c2 are in G.P.

Q5.  Let a and b be roots of x2-3x+p=0 and let c and d be the roots of x2-12x+q=0 where a, b, c, d form an increasing G.P. Then the ratio of (q + p) : (q – p) is equal to

•  8 : 7
•  11:10
•  17:15
•  None of these

17:15

Q6.  If the roots of the cubic equation ax3+bx2+cx+d=0 are in G.P., then

•  ca3=b3d
•   c3a=bd3
•  ab3=c3d
•  a3b=cd3

ca3=b3d

Q7.  If x1,x2,x3 as well as y1,y2,y3 are in G.P. with the same common ratio, then the points (x1,y1), (x2,y2) and (x3, y3) and

•   Lie on a straight line
•  Lie on an ellipse
•  Lie on a circle
•  Are vertices of a triangle

Lie on a straight line

Q8.  Let f(x)=2x+1, Then the number of real values of x for which the three unequal numbers f(x),f(2x),f(4x) are in GP is

•  1
•   2
•   0
•   None of these

0

Q9.  If a1/x = b1/y = c1/z and a,b,c are in G.P., then x, y, z will be in

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

A.P.

Q10.  If x, y, z are in G.P. and ax = by = cz , then

•   logac = logcb
•   logba = logcb
•   logbc = logab
•   None of these

logba = logcb

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