Question

What is the 11th term of the A.P. \( 3, -3, -\frac{1}{2}, 2, \dots \)?

• A. \( 28 \)
• B. \( 22 \)
• C. \( -38 \)
• D. \( -57 \)

Hint:

The \( n \)th term formula for an A.P. is \( a_n = a + (n-1)d \).

Answer 1

The Correct Option is D

Step 1: Identify given values In an arithmetic progression (A.P.), the \( n \)th term is given by: \[ a_n = a + (n-1) d \] where: - First term \( a = 3 \) - Second term \( a_2 = -3 \), so common difference: \[ d = -3 - 3 = -6 \] Step 2: Find the 11th term \[ a_{11} = 3 + (11-1)(-6) \] \[ = 3 + 10(-6) \] \[ = 3 - 60 \] \[ = -57 \] Thus, the correct answer is \( -57 \).