The third term of Geometric Progression is 4. The product of the five terms is

a)

b)

c)

d)

The rational number which equals the numbers with recurring decimals is

a)

b)

c)

d)

If a, b, c are in Geometric Progression then the equations  
have a common root if  are in

a) Arithmetic Progression

b) Geometric Progression

c) Harmonic Progression

d) None of these

If a, b, c, d and p are distinct real numbers such that
 
then a, b, c, d

a) Are in Arithmetic Progression

b) Are in Geometric Progression

c) Are in Harmonic Progression

d) Satisfy ab = cd

e) Satisfy none of these

Sum of the first n terms of the series  is

a) 2ⁿ – n – 1

b) 1 – 2^{− n}

c) n + 2^{− n} – 1

d) 2ⁿ + 1

If  are in Arithmetic Progression
then

a) a, b, c are in Arithmetic Progression

b)  are in  Arithmetic Progression

c) a, b, c are in Geometric Progression

d) a, b, c are in Harmonic Progression

Let T_r be the r^th term of an Arithmetic Progression for  If for some positive integers m, n we have  and  then T_mn equals

a)

b)

c)

d)

If  are in Geometric Progression then
 are in

a) Arithmetic Progression

b) Geometric Progression

c) Harmonic Progression

d) None of these

Let  be in Arithmetic Progression and
 be in Harmonic Progression. If  and
 then  is

a) 2

b) 3

c) 5

d) 6

The harmonic means of the roots of the equation
 is

a) 2

b) 4

c) 6

d) 8

Consider an infinite geometric series with first term a and common ratio r. If its sum is four and the second term is  then

a)

b)

c)

d)

Let the positive numbers a, b, c, d be in Arithmetic Progression. Then
abc, abd, acd, bcd are

a) Not in Arithmetic Progression/Geometric Progression/Harmonic Progression

b) In Arithmetic Progression

c) In Geometric Progression

d) In Harmonic Progression

If  are positive real numbers whose product is a fixed number c then the minimum value of
  is

a)

b)

c)

d)

Suppose a, b, c are in Arithmetic Progression and  are in Geometric Progression. If  then the value of a is

a)

b)

c)

d)

An infinite Geometric Progression has first term x and sum 5 then

a)

b)

c)

d)

If α, β are roots of  and  are in Geometric Progression and  then

a)

b)

c)

d)

Multiple Choice

For  if
 , then

a)  

b)  

c)  

d)  

If x, y, z are in Harmonic Progression then show that
 

If the m^th, n^th and p^th term of an Arithmetic Progression and a Geometric Progression are equal and are x, y, z then prove that
 

The angles of a triangle are in Arithmetic Progression and let . Find the angle A.

If  are in Arithmetic Progression where  for all i, show that
 

Find three numbers a, b, c between 2 and 18 such that (i) their sum is 25 (ii) 2, a, b are consecutive terms of an Arithmetic Progression and (iii) the numbers b, c, 18 are consecutive terms of a Geometric Progression

The sum of the squares of three distinct real numbers which are in Geometric Progression is . If their sum is , show that