Question

The number of terms in the A.P. \( 41, 38, 35, \dots, 8 \) is:

• A. \( 12 \)
• B. \( 14 \)
• C. \( 10 \)
• D. \( 15 \)

Hint:

Use \( a_n = a + (n-1)d \) to find the number of terms in an arithmetic sequence.

Answer 1

The Correct Option is A

Step 1: Identify given values First term: \( a = 41 \) Common difference: \( d = 38 - 41 = -3 \) Last term: \( l = 8 \) Step 2: Use the nth term formula \[ a_n = a + (n-1)d \] Setting \( a_n = 8 \): \[ 8 = 41 + (n-1)(-3) \] \[ 8 - 41 = (n-1)(-3) \] \[ -33 = (n-1)(-3) \] \[ n-1 = 11 \] \[ n = 12 \] Thus, the correct answer is \( 12 \).