Arithmetic Progressions Test

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Arithmetic Progressions Test - 1

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Question 1
1 / -0

Progressions with equal common difference are known as

A
none of these

B
Geometric Progression

C
Harmonic Progression

D
Arithmetic Progression

Solution

Explanation:

Progressions with equal common difference are known as Arithmetic Progression. i.e the difference between any two consecutive terms is constant throughout the series, this constant difference is called common difference usally denoted by the letter d

if a is the 1st term , d is the common difference , then the AP is represented by a , a+d , a+2d , a+3d ...... ......................................... a+(n−1)d
Question 2
1 / -0

If a, b and c are in A.P., then the relation between them is given by

A
2c = a + b

B
2a = b + c

C
a = b + c

D
2b = a + c

Solution

Explanation:

We know that if a, b, c, .... are in AP then 2nd term - 1st term = 3rd term - 2nd term
b - a = c - b
=> 2b = a + c
Question 3
1 / -0

If a, b and c are in A.P, then b =

A
a+c/2

B
a−c/2

C
c−a/2

D
none of these

Solution

Explanation:

If a,b and cc are in A.P., then

b - a = c - b

2b = a + c

b=a+c/2
Question 4
1 / -0

The common difference of the A.P. can be

A
only negative

B
only zero

C
only positive

D
positive, negative or zero

Solution

Explanation:

The common difference of the A.P. can be positive, e.g. 1, 2, 3, 4 ..... d is +ve and series is increasing

negative e.g 4, 3, 2, 1 ...... d is - ve and series is decreasing

or zero also and the AP becomes constant e.g 4, 4, 4, 4 ...... .