Question

Select the set of numbers that forms an AP.

• A. 1, 3, 5, 7,...
• B. 1, 4, 5, 8, ...
• C. 0, 1, 3, 5, ...
• D. 2, 4, 6, 8,...

Answer 1

Answer: (A), (D)

The correct options are
A

1, 3, 5, 7,...

D

2, 4, 6, 8,...

A sequence of numbers in which each term differs from the preceding one by a constant quantity (common difference) is called as an arithmetic progression.

Consider the AP: 1, 3, 5, 7,...

first term $a_1$ = 1

second term $a_2$ = 3

third term $a_3$ = 5

$a_2$ - $a_1$ = 3 - 1 = 2

$a_3$ - $a_2$ = 5 - 3 = 2

$\therefore$ common difference d = 2

Consider the AP: 2, 4, 6, 8,..

first term $a_1$ = 2

second term $a_2$ = 4

third term $a_3$ = 6

$a_2$ - $a_1$ = 4 - 2 = 2

$a_3$ - $a_2$ = 6 - 4 = 2

$\therefore$ common difference d = 2

Among the given options, the set of numbers 1, 3, 5, 7,... and 2, 4, 6, 8,... have a constant common difference between them which is 2. Hence these sets form an AP.