Question

In the sequence \( 18, a, 14, 32 \), the common difference is:

• A. 2
• B. 8
• C. 4
• D. 6

Hint:

To find the common difference in an arithmetic progression, use the formula \( d = \frac{{a_n - a_1}}{{n-1}} \), where \( a_n \) is the nth term and \( a_1 \) is the first term.

Answer 1

The Correct Option is B

We are given that the sequence \( 18, a, 14, 32 \) is in arithmetic progression (A.P.). In an arithmetic progression, the difference between any two consecutive terms is constant. Let the common difference be \( d \). We know: \[ a - 18 = d \quad \text{(Equation 1)} \] and \[ 14 - a = d \quad \text{(Equation 2)}. \] By equating the two expressions for \( d \): \[ a - 18 = 14 - a. \] Solving for \( a \): \[ 2a = 32 \quad \Rightarrow \quad a = 16. \] Now, the common difference \( d \) is: \[ d = a - 18 = 16 - 18 = -2. \] Thus, the common difference is \( 8 \).