Question

Common difference of the AP \( 3, 1, -1, -3, \dots \) is

• A. \( 1 \)
• B. \( -2 \)
• C. \( -1 \)
• D. \( 2 \)

Hint:

The common difference of an arithmetic progression is constant throughout the sequence. To find it, subtract any term from its succeeding term.

Answer 1

The Correct Option is B

Step 1: Identify consecutive terms.
In the given arithmetic progression \( 3, 1, -1, -3, \dots \), the consecutive terms are \( a_1 = 3 \), \( a_2 = 1 \), \( a_3 = -1 \), \( a_4 = -3 \), and so on. Step 2: Calculate the common difference.
The common difference \( d \) of an arithmetic progression is the difference between any two consecutive terms: \( d = a_{n+1} - a_n \). We can calculate the common difference using the first two terms: \[ d = a_2 - a_1 = 1 - 3 = -2 \] We can verify this using other consecutive terms: \[ d = a_3 - a_2 = -1 - 1 = -2 \] \[ d = a_4 - a_3 = -3 - (-1) = -3 + 1 = -2 \] The common difference of the arithmetic progression is \( -2 \).