Find the number of terms in the following arithmetic progression: \( 3,9,15,21, \ldots, 81 \) A. 11 B. 8 C. 17 D. 14

To find the number of terms in the arithmetic progression (AP) given, we first identify the first term \( a \) and the common difference \( d \). The first term \( a = 3 \), and the common difference \( d = 9 - 3 = 6 \). The nth term of an AP can be expressed as: \[ a_n = a + (n-1)d \] Setting \( a_n \) equal to the last term \( 81 \): \[ 81 = 3 + (n-1) \cdot 6 \] Subtracting 3 from both sides yields: \[ 78 = (n-1) \cdot 6 \] Dividing both sides by 6 gives: \[ 13 = n - 1 \] Adding 1 to both sides results in: \[ n = 14 \] Thus, the number of terms in this arithmetic progression is \( \boxed{14} \).