Find the number of terms in the following arithmetic progression: \( 3,9,15,21, \ldots, 87 \) A. 9 B. 12 C. 18 D. 15

To find the number of terms in the arithmetic progression \( 3, 9, 15, 21, \ldots, 87 \), we first identify the first term \( a \) and the common difference \( d \). The first term: \[ a = 3 \] The common difference: \[ d = 9 - 3 = 6 \] The general formula for the \( n \)-th term of an arithmetic progression is: \[ a_n = a + (n-1)d \] Setting \( a_n = 87 \) (the last term), we can solve for \( n \): \[ 87 = 3 + (n-1)6 \] Subtract \( 3 \) from both sides: \[ 84 = (n-1)6 \] Now, divide by \( 6 \): \[ 14 = n - 1 \] Finally, add \( 1 \) to find \( n \): \[ n = 15 \] Thus, the number of terms in the arithmetic progression is \( \boxed{15} \).