## Properties of A.P. - Advance

An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant. For example, the sequence 1, 2, 3, 4, ... is an arithmetic progression with common difference 1. Second example: the sequence 3, 5, 7, 9, 11,... is an arithmetic progression. with common difference 2

Q1.  If the sum of the roots of the equation ax2+bx+c =0 be equal to the sum of the reciprocals of their squares, then bc2, ca2, ab2 will be in

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

A.P.

Q2.  If a, b, c are in A.P., then the straight line ax + by + c = 0 will always pass through the point

•   (-1,-2)
•  (1,-2)
•  (1,2)
•  (-1,-2)

(1,-2)

Q3.  If a, b, c, d, e, f are in A.P., then the value of e – c will be

•  2 (c – a)
•   2 (f – d)
•  2 (d – c)
•   (d-c)

2(d-c)

Q4.  Given where a, b, c, d are real numbers, then

•   a, b, c, d are in A.P.
•   1/a, 1/b, 1/c, 1/d are in A.P.
•   (a+b) , (b+c), (c+d) , (d+a) are in A.P.
•  None of these

1/a, 1/b, 1/c, 1/d are in A.P.

Q5.  If a, b, c are in A.P., then (a + 2b – c) (2b+ c – a) (c + a – b) equals

•  abc
•  abc/2
•  abc/3
•  4abc

4abc

Q6.  If a, b, c, d, e are in A.P. then the value of a+b+4c – 4d + e in terms of a, if possible is

•  2a
•   4a
•  3
•  None of these

None of these

Q7.  If a, b, c are in A.P. then the equation (a-b)2+(c-a_x+(b-c)=0 has two roots which are

•   Rational and equal
•  Rational and distinct
•   Irrational conjugates
•  Complex conjugates

Rational and equal

Q8.  If the sides of a right angled triangle are in A.P., then the sides are proportional to

•  1,2,3
•   4,5,6
•   3,4,5
•   None of these

3,4,5

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