Question

If A, B and C are three arithmetic progressions (APs) as given below:

A = 2, 4, 6, 8, ....... upto n terms 

B = 3, 6, 9, 12, ....... upto n terms 

C = 0, 4, 8, 12, ....... upto n terms, then out of A + B, A − C, C − B and B – А which is/are A.P.?

Options

• A + B

• A − C

• C − B

• all are A.P.

Answer 1

all are A.P.

Explanation:

Given,

A = 2, 4, 6, 8, ........ upto n terms

B = 3, 6, 9, 12, ...... upto n terms

C = 0, 4, 8, 12, ...... upto n terms, then

A + B = 2 + 3, 4 + 6, 6 + 9, 8 + 12, ........

= 5, 10, 15, 20, ..........

The above list is an A.P. with common difference = 5.

A − C = 2 − 0, 4 − 4, 6 − 8, 8 − 12, ......

= 2, 0, −2, -4, .........

The above list is an A.P. with common difference = -2.

C − B = 0 − 3, 4 − 6, 8 − 9, 12 − 12, .........

= -3, −2, −1, 0, .........

The above list is an A.P. with common difference = 1.